LMFDB - Embedded newform 315.2.l.c.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(121,315)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	315.151
Dual form			315.2.l.c.121.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65219 q^{2} +(1.69529 - 0.354953i) q^{3} +5.03414 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-4.49624 + 0.941405i) q^{6} +(-1.76710 - 1.96910i) q^{7} -8.04712 q^{8} +(2.74802 - 1.20350i) q^{9} +O(q^{10})$	\(q-2.65219 q^{2} +(1.69529 - 0.354953i) q^{3} +5.03414 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-4.49624 + 0.941405i) q^{6} +(-1.76710 - 1.96910i) q^{7} -8.04712 q^{8} +(2.74802 - 1.20350i) q^{9} +(1.32610 - 2.29687i) q^{10} +(-2.66493 - 4.61580i) q^{11} +(8.53432 - 1.78688i) q^{12} +(-2.30157 - 3.98643i) q^{13} +(4.68669 + 5.22244i) q^{14} +(-0.540247 + 1.64564i) q^{15} +11.2743 q^{16} +(-0.923899 + 1.60024i) q^{17} +(-7.28827 + 3.19191i) q^{18} +(1.39618 + 2.41825i) q^{19} +(-2.51707 + 4.35969i) q^{20} +(-3.69468 - 2.71096i) q^{21} +(7.06792 + 12.2420i) q^{22} +(0.852128 - 1.47593i) q^{23} +(-13.6422 + 2.85635i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(6.10421 + 10.5728i) q^{26} +(4.23150 - 3.01569i) q^{27} +(-8.89581 - 9.91273i) q^{28} +(2.11711 - 3.66695i) q^{29} +(1.43284 - 4.36456i) q^{30} +3.69376 q^{31} -13.8073 q^{32} +(-6.15622 - 6.87919i) q^{33} +(2.45036 - 4.24415i) q^{34} +(2.58884 - 0.545800i) q^{35} +(13.8339 - 6.05857i) q^{36} +(-5.06506 - 8.77294i) q^{37} +(-3.70294 - 6.41367i) q^{38} +(-5.31683 - 5.94121i) q^{39} +(4.02356 - 6.96901i) q^{40} +(-1.59776 - 2.76740i) q^{41} +(9.79902 + 7.19000i) q^{42} +(-4.34272 + 7.52182i) q^{43} +(-13.4156 - 23.2366i) q^{44} +(-0.331749 + 2.98160i) q^{45} +(-2.26001 + 3.91445i) q^{46} +10.7100 q^{47} +(19.1131 - 4.00183i) q^{48} +(-0.754734 + 6.95919i) q^{49} +(1.32610 + 2.29687i) q^{50} +(-0.998267 + 3.04081i) q^{51} +(-11.5864 - 20.0683i) q^{52} +(1.74772 - 3.02714i) q^{53} +(-11.2228 + 7.99821i) q^{54} +5.32986 q^{55} +(14.2200 + 15.8456i) q^{56} +(3.22529 + 3.60406i) q^{57} +(-5.61499 + 9.72546i) q^{58} -1.93055 q^{59} +(-2.71968 + 8.28438i) q^{60} -2.89482 q^{61} -9.79658 q^{62} +(-7.22582 - 3.28443i) q^{63} +14.0711 q^{64} +4.60314 q^{65} +(16.3275 + 18.2449i) q^{66} +1.65653 q^{67} +(-4.65104 + 8.05583i) q^{68} +(0.920719 - 2.80459i) q^{69} +(-6.86611 + 1.44757i) q^{70} -2.79922 q^{71} +(-22.1136 + 9.68469i) q^{72} +(-1.45087 + 2.51299i) q^{73} +(13.4335 + 23.2675i) q^{74} +(-1.15504 - 1.29069i) q^{75} +(7.02855 + 12.1738i) q^{76} +(-4.37979 + 13.4041i) q^{77} +(14.1013 + 15.7573i) q^{78} +8.65071 q^{79} +(-5.63713 + 9.76380i) q^{80} +(6.10319 - 6.61446i) q^{81} +(4.23757 + 7.33969i) q^{82} +(2.26167 - 3.91732i) q^{83} +(-18.5995 - 13.6474i) q^{84} +(-0.923899 - 1.60024i) q^{85} +(11.5177 - 19.9493i) q^{86} +(2.28753 - 6.96801i) q^{87} +(21.4450 + 37.1439i) q^{88} +(3.12944 + 5.42035i) q^{89} +(0.879863 - 7.90779i) q^{90} +(-3.78260 + 11.5764i) q^{91} +(4.28973 - 7.43003i) q^{92} +(6.26200 - 1.31111i) q^{93} -28.4050 q^{94} -2.79236 q^{95} +(-23.4074 + 4.90094i) q^{96} +(-4.38018 + 7.58670i) q^{97} +(2.00170 - 18.4571i) q^{98} +(-12.8784 - 9.47705i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) $ 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−2.65219			−1.87538			−0.937692	−	0.347466i	$-0.887042\pi$
$2$	−2.65219			−1.87538			−0.937692	+	0.347466i	$0.887042\pi$
$3$	1.69529	−	0.354953i	0.978776	−	0.204932i
$3$	1.69529	−	0.354953i	0.978776	−	0.204932i
$4$	5.03414			2.51707
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	−4.49624	+	0.941405i	−1.83558	+	0.384327i
$7$	−1.76710	−	1.96910i	−0.667900	−	0.744251i
$7$	−1.76710	−	1.96910i	−0.667900	−	0.744251i
$8$	−8.04712			−2.84509
$9$	2.74802	−	1.20350i	0.916005	−	0.401166i
$10$	1.32610	−	2.29687i	0.419349	−	0.726333i
$11$	−2.66493	−	4.61580i	−0.803507	−	1.39171i	−0.917294	−	0.398210i	$-0.869632\pi$
$11$	−2.66493	−	4.61580i	−0.803507	−	1.39171i	0.113787	−	0.993505i	$-0.463702\pi$
$12$	8.53432	−	1.78688i	2.46365	−	0.515829i
$13$	−2.30157	−	3.98643i	−0.638340	−	1.10564i	−0.985797	−	0.167942i	$-0.946288\pi$
$13$	−2.30157	−	3.98643i	−0.638340	−	1.10564i	0.347456	−	0.937696i	$-0.387045\pi$
$14$	4.68669	+	5.22244i	1.25257	+	1.39576i
$15$	−0.540247	+	1.64564i	−0.139491	+	0.424903i
$16$	11.2743			2.81857
$17$	−0.923899	+	1.60024i	−0.224078	+	0.388115i	−0.956043	−	0.293228i	$-0.905271\pi$
$17$	−0.923899	+	1.60024i	−0.224078	+	0.388115i	0.731964	+	0.681343i	$0.238604\pi$
$18$	−7.28827	+	3.19191i	−1.71786	+	0.752340i
$19$	1.39618	+	2.41825i	0.320305	+	0.554785i	0.980551	−	0.196265i	$-0.0628812\pi$
$19$	1.39618	+	2.41825i	0.320305	+	0.554785i	−0.660246	+	0.751050i	$0.729548\pi$
$20$	−2.51707	+	4.35969i	−0.562834	+	0.974856i
$21$	−3.69468	−	2.71096i	−0.806246	−	0.591581i
$22$	7.06792	+	12.2420i	1.50688	+	2.61000i
$23$	0.852128	−	1.47593i	0.177681	−	0.307753i	−0.763405	−	0.645920i	$-0.776474\pi$
$23$	0.852128	−	1.47593i	0.177681	−	0.307753i	0.941086	+	0.338168i	$0.109807\pi$
$24$	−13.6422	+	2.85635i	−2.78470	+	0.583050i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	6.10421	+	10.5728i	1.19713	+	2.07350i
$27$	4.23150	−	3.01569i	0.814353	−	0.580371i
$28$	−8.89581	−	9.91273i	−1.68115	−	1.87333i
$29$	2.11711	−	3.66695i	0.393138	−	0.680935i	−0.599724	−	0.800207i	$-0.704723\pi$
$29$	2.11711	−	3.66695i	0.393138	−	0.680935i	0.992862	+	0.119272i	$0.0380562\pi$
$30$	1.43284	−	4.36456i	0.261599	−	0.796856i
$31$	3.69376			0.663419			0.331710	−	0.943382i	$-0.392375\pi$
$31$	3.69376			0.663419			0.331710	+	0.943382i	$0.392375\pi$
$32$	−13.8073			−2.44081
$33$	−6.15622	−	6.87919i	−1.07166	−	1.19751i
$34$	2.45036	−	4.24415i	0.420233	−	0.727866i
$35$	2.58884	−	0.545800i	0.437594	−	0.0922570i
$36$	13.8339	−	6.05857i	2.30565	−	1.00976i
$37$	−5.06506	−	8.77294i	−0.832690	−	1.44226i	−0.895897	−	0.444261i	$-0.853466\pi$
$37$	−5.06506	−	8.77294i	−0.832690	−	1.44226i	0.0632070	−	0.998000i	$-0.479867\pi$
$38$	−3.70294	−	6.41367i	−0.600695	−	1.04044i
$39$	−5.31683	−	5.94121i	−0.851373	−	0.951356i
$40$	4.02356	−	6.96901i	0.636181	−	1.10190i
$41$	−1.59776	−	2.76740i	−0.249528	−	0.432196i	0.713867	−	0.700282i	$-0.246942\pi$
$41$	−1.59776	−	2.76740i	−0.249528	−	0.432196i	−0.963395	+	0.268086i	$0.913609\pi$
$42$	9.79902	+	7.19000i	1.51202	+	1.10944i
$43$	−4.34272	+	7.52182i	−0.662259	+	1.14707i	0.317762	+	0.948171i	$0.397069\pi$
$43$	−4.34272	+	7.52182i	−0.662259	+	1.14707i	−0.980021	+	0.198896i	$0.936264\pi$
$44$	−13.4156	−	23.2366i	−2.02248	−	3.50304i
$45$	−0.331749	+	2.98160i	−0.0494542	+	0.444471i
$46$	−2.26001	+	3.91445i	−0.333220	+	0.577154i
$47$	10.7100			1.56221			0.781107	−	0.624397i	$-0.214655\pi$
$47$	10.7100			1.56221			0.781107	+	0.624397i	$0.214655\pi$
$48$	19.1131	−	4.00183i	2.75874	−	0.577615i
$49$	−0.754734	+	6.95919i	−0.107819	+	0.994171i
$50$	1.32610	+	2.29687i	0.187538	+	0.324826i
$51$	−0.998267	+	3.04081i	−0.139785	+	0.425799i
$52$	−11.5864	−	20.0683i	−1.60675	−	2.78297i
$53$	1.74772	−	3.02714i	0.240068	−	0.415810i	−0.720666	−	0.693283i	$-0.756164\pi$
$53$	1.74772	−	3.02714i	0.240068	−	0.415810i	0.960733	+	0.277473i	$0.0894970\pi$
$54$	−11.2228	+	7.99821i	−1.52722	+	1.08842i
$55$	5.32986			0.718679
$56$	14.2200	+	15.8456i	1.90023	+	2.11746i
$57$	3.22529	+	3.60406i	0.427200	+	0.477369i
$58$	−5.61499	+	9.72546i	−0.737285	+	1.27702i
$59$	−1.93055			−0.251336			−0.125668	−	0.992072i	$-0.540107\pi$
$59$	−1.93055			−0.251336			−0.125668	+	0.992072i	$0.540107\pi$
$60$	−2.71968	+	8.28438i	−0.351109	+	1.06951i
$61$	−2.89482			−0.370643			−0.185322	−	0.982678i	$-0.559333\pi$
$61$	−2.89482			−0.370643			−0.185322	+	0.982678i	$0.559333\pi$
$62$	−9.79658			−1.24417
$63$	−7.22582	−	3.28443i	−0.910368	−	0.413799i
$64$	14.0711			1.75889
$65$	4.60314			0.570949
$66$	16.3275	+	18.2449i	2.00978	+	2.24580i
$67$	1.65653			0.202378			0.101189	−	0.994867i	$-0.467735\pi$
$67$	1.65653			0.202378			0.101189	+	0.994867i	$0.467735\pi$
$68$	−4.65104	+	8.05583i	−0.564021	+	0.976913i
$69$	0.920719	−	2.80459i	0.110841	−	0.337633i
$70$	−6.86611	+	1.44757i	−0.820657	+	0.173017i
$71$	−2.79922			−0.332207			−0.166103	−	0.986108i	$-0.553119\pi$
$71$	−2.79922			−0.332207			−0.166103	+	0.986108i	$0.553119\pi$
$72$	−22.1136	+	9.68469i	−2.60612	+	1.14135i
$73$	−1.45087	+	2.51299i	−0.169812	+	0.294123i	−0.938354	−	0.345677i	$-0.887649\pi$
$73$	−1.45087	+	2.51299i	−0.169812	+	0.294123i	0.768542	+	0.639800i	$0.220983\pi$
$74$	13.4335	+	23.2675i	1.56161	+	2.70480i
$75$	−1.15504	−	1.29069i	−0.133373	−	0.149036i
$76$	7.02855	+	12.1738i	0.806230	+	1.39643i
$77$	−4.37979	+	13.4041i	−0.499123	+	1.52754i
$78$	14.1013	+	15.7573i	1.59665	+	1.78416i
$79$	8.65071			0.973281			0.486641	−	0.873602i	$-0.338222\pi$
$79$	8.65071			0.973281			0.486641	+	0.873602i	$0.338222\pi$
$80$	−5.63713	+	9.76380i	−0.630250	+	1.09163i
$81$	6.10319	−	6.61446i	0.678132	−	0.734940i
$82$	4.23757	+	7.33969i	0.467961	+	0.810533i
$83$	2.26167	−	3.91732i	0.248250	−	0.429982i	−0.714790	−	0.699339i	$-0.753478\pi$
$83$	2.26167	−	3.91732i	0.248250	−	0.429982i	0.963040	+	0.269357i	$0.0868111\pi$
$84$	−18.5995	−	13.6474i	−2.02938	−	1.48905i
$85$	−0.923899	−	1.60024i	−0.100211	−	0.173570i
$86$	11.5177	−	19.9493i	1.24199	−	2.15119i
$87$	2.28753	−	6.96801i	0.245248	−	0.747049i
$88$	21.4450	+	37.1439i	2.28605	+	3.95955i
$89$	3.12944	+	5.42035i	0.331720	+	0.574556i	0.982849	−	0.184411i	$-0.0590378\pi$
$89$	3.12944	+	5.42035i	0.331720	+	0.574556i	−0.651129	+	0.758967i	$0.725704\pi$
$90$	0.879863	−	7.90779i	0.0927457	−	0.833554i
$91$	−3.78260	+	11.5764i	−0.396525	+	1.21354i
$92$	4.28973	−	7.43003i	0.447235	−	0.774634i
$93$	6.26200	−	1.31111i	0.649339	−	0.135956i
$94$	−28.4050			−2.92975
$95$	−2.79236			−0.286490
$96$	−23.4074	+	4.90094i	−2.38900	+	0.500200i
$97$	−4.38018	+	7.58670i	−0.444740	+	0.770312i	−0.998034	−	0.0626738i	$-0.980037\pi$
$97$	−4.38018	+	7.58670i	−0.444740	+	0.770312i	0.553294	+	0.832986i	$0.313371\pi$
$98$	2.00170	−	18.4571i	0.202202	−	1.86445i
$99$	−12.8784	−	9.47705i	−1.29433	−	0.952479i
$100$	−2.51707	−	4.35969i	−0.251707	−	0.435969i
$101$	−3.28329	−	5.68683i	−0.326700	−	0.565861i	0.655155	−	0.755494i	$-0.272603\pi$
$101$	−3.28329	−	5.68683i	−0.326700	−	0.565861i	−0.981855	+	0.189634i	$0.939270\pi$
$102$	2.64760	−	8.06483i	0.262151	−	0.798537i
$103$	0.584477	−	1.01234i	0.0575902	−	0.0997492i	−0.835793	−	0.549045i	$-0.814992\pi$
$103$	0.584477	−	1.01234i	0.0575902	−	0.0997492i	0.893383	+	0.449296i	$0.148325\pi$
$104$	18.5210	+	32.0793i	1.81613	+	3.14564i
$105$	4.19510	−	1.84421i	0.409400	−	0.179976i
$106$	−4.63529	+	8.02856i	−0.450220	+	0.779803i
$107$	6.79339	+	11.7665i	0.656742	+	1.13751i	0.981454	+	0.191698i	$0.0613993\pi$
$107$	6.79339	+	11.7665i	0.656742	+	1.13751i	−0.324712	+	0.945813i	$0.605267\pi$
$108$	21.3019	−	15.1814i	2.04978	−	1.46083i
$109$	1.93478	−	3.35114i	0.185318	−	0.320981i	−0.758365	−	0.651830i	$-0.774002\pi$
$109$	1.93478	−	3.35114i	0.185318	−	0.320981i	0.943684	+	0.330849i	$0.107335\pi$
$110$	−14.1358			−1.34780
$111$	−11.7007	−	13.0748i	−1.11058	−	1.24101i
$112$	−19.9227	−	22.2002i	−1.88252	−	2.09772i
$113$	2.48797	+	4.30929i	0.234048	+	0.405383i	0.958996	−	0.283421i	$-0.0914693\pi$
$113$	2.48797	+	4.30929i	0.234048	+	0.405383i	−0.724947	+	0.688804i	$0.758136\pi$
$114$	−8.55410	−	9.55867i	−0.801165	−	0.895251i
$115$	0.852128	+	1.47593i	0.0794614	+	0.137631i
$116$	10.6578	−	18.4599i	0.989555	−	1.71396i
$117$	−11.1224	−	8.18486i	−1.02827	−	0.756690i
$118$	5.12019			0.471351
$119$	4.78366	−	1.00853i	0.438517	−	0.0924516i
$120$	4.34743	−	13.2427i	0.396864	−	1.20889i
$121$	−8.70372	+	15.0753i	−0.791247	+	1.37048i
$122$	7.67762			0.695099
$123$	−3.69096	−	4.12442i	−0.332803	−	0.371886i
$124$	18.5949			1.66987
$125$	1.00000			0.0894427
$126$	19.1643	+	8.71095i	1.70729	+	0.776033i
$127$	13.5309			1.20067			0.600337	−	0.799747i	$-0.295033\pi$
$127$	13.5309			1.20067			0.600337	+	0.799747i	$0.295033\pi$
$128$	−9.70473			−0.857785
$129$	−4.69228	+	14.2931i	−0.413132	+	1.25844i
$130$	−12.2084			−1.07075
$131$	1.86661	−	3.23306i	0.163087	−	0.282474i	−0.772888	−	0.634543i	$-0.781188\pi$
$131$	1.86661	−	3.23306i	0.163087	−	0.282474i	0.935974	+	0.352069i	$0.114522\pi$
$132$	−30.9913	−	34.6308i	−2.69744	−	3.01422i
$133$	2.29460	−	7.02250i	0.198967	−	0.608928i
$134$	−4.39345			−0.379536
$135$	0.495918	+	5.17243i	0.0426818	+	0.445172i
$136$	7.43473	−	12.8773i	0.637523	−	1.10422i
$137$	−1.16437	−	2.01675i	−0.0994791	−	0.172303i	0.811990	−	0.583671i	$-0.198384\pi$
$137$	−1.16437	−	2.01675i	−0.0994791	−	0.172303i	−0.911469	+	0.411368i	$0.865051\pi$
$138$	−2.44192	+	7.43833i	−0.207870	+	0.633193i
$139$	−2.92543	−	5.06699i	−0.248132	−	0.429777i	0.714876	−	0.699252i	$-0.246483\pi$
$139$	−2.92543	−	5.06699i	−0.248132	−	0.429777i	−0.963007	+	0.269475i	$0.913150\pi$
$140$	13.0326	−	2.74763i	1.10145	−	0.232217i
$141$	18.1566	−	3.80155i	1.52906	−	0.320148i
$142$	7.42409			0.623016
$143$	−12.2670	+	21.2472i	−1.02582	+	1.77678i
$144$	30.9819	−	13.5685i	2.58182	−	1.13071i
$145$	2.11711	+	3.66695i	0.175817	+	0.304523i
$146$	3.84800	−	6.66493i	0.318463	−	0.551594i
$147$	1.19069	+	12.0657i	0.0982068	+	0.995166i
$148$	−25.4982	−	44.1642i	−2.09594	−	3.63027i
$149$	−1.51767	+	2.62868i	−0.124332	+	0.215350i	−0.921472	−	0.388445i	$-0.873012\pi$
$149$	−1.51767	+	2.62868i	−0.124332	+	0.215350i	0.797140	+	0.603795i	$0.206346\pi$
$150$	3.06340	+	3.42315i	0.250126	+	0.279499i
$151$	−1.63949	−	2.83968i	−0.133420	−	0.231090i	0.791573	−	0.611075i	$-0.209263\pi$
$151$	−1.63949	−	2.83968i	−0.133420	−	0.231090i	−0.924993	+	0.379985i	$0.875929\pi$
$152$	−11.2352	−	19.4600i	−0.911296	−	1.57841i
$153$	−0.613006	+	5.50940i	−0.0495586	+	0.445408i
$154$	11.6160	−	35.5502i	0.936048	−	2.86472i
$155$	−1.84688	+	3.19889i	−0.148345	+	0.256941i
$156$	−26.7656	−	29.9089i	−2.14297	−	2.39463i
$157$	19.1658			1.52960			0.764800	−	0.644268i	$-0.222838\pi$
$157$	19.1658			1.52960			0.764800	+	0.644268i	$0.222838\pi$
$158$	−22.9434			−1.82528
$159$	1.88840	−	5.75224i	0.149760	−	0.456182i
$160$	6.90365	−	11.9575i	0.545781	−	0.945321i
$161$	−4.41205	+	0.930182i	−0.347718	+	0.0733086i
$162$	−16.1868	+	17.5428i	−1.27176	+	1.37830i
$163$	5.13329	+	8.89111i	0.402070	+	0.696406i	0.993976	−	0.109602i	$-0.0349575\pi$
$163$	5.13329	+	8.89111i	0.402070	+	0.696406i	−0.591906	+	0.806007i	$0.701624\pi$
$164$	−8.04334	−	13.9315i	−0.628080	−	1.08787i
$165$	9.03566	−	1.89185i	0.703425	−	0.147280i
$166$	−5.99838	+	10.3895i	−0.465565	+	0.806382i
$167$	7.65659	+	13.2616i	0.592485	+	1.02621i	0.993897	+	0.110316i	$0.0351864\pi$
$167$	7.65659	+	13.2616i	0.592485	+	1.02621i	−0.401411	+	0.915898i	$0.631480\pi$
$168$	29.7316	+	21.8155i	2.29384	+	1.68310i
$169$	−4.09444	+	7.09178i	−0.314957	+	0.545522i
$170$	2.45036	+	4.24415i	0.187934	+	0.325511i
$171$	6.74708	+	4.96510i	0.515962	+	0.379690i
$172$	−21.8619	+	37.8659i	−1.66695	+	2.88724i
$173$	17.2221			1.30937			0.654684	−	0.755902i	$-0.272802\pi$
$173$	17.2221			1.30937			0.654684	+	0.755902i	$0.272802\pi$
$174$	−6.06696	+	18.4805i	−0.459935	+	1.40101i
$175$	−0.821745	+	2.51490i	−0.0621181	+	0.190109i
$176$	−30.0451	−	52.0397i	−2.26474	−	3.92264i
$177$	−3.27284	+	0.685254i	−0.246001	+	0.0515068i
$178$	−8.29988	−	14.3758i	−0.622102	−	1.07751i
$179$	−12.8188	+	22.2029i	−0.958125	+	1.65952i	−0.231076	+	0.972936i	$0.574224\pi$
$179$	−12.8188	+	22.2029i	−0.958125	+	1.65952i	−0.727049	+	0.686585i	$0.759109\pi$
$180$	−1.67007	+	15.0098i	−0.124480	+	1.11876i
$181$	−20.6995			−1.53858			−0.769290	−	0.638900i	$-0.779390\pi$
$181$	−20.6995			−1.53858			−0.769290	+	0.638900i	$0.779390\pi$
$182$	10.0322	−	30.7030i	0.743636	−	2.27586i
$183$	−4.90755	+	1.02752i	−0.362777	+	0.0759568i
$184$	−6.85718	+	11.8770i	−0.505518	+	0.875583i
$185$	10.1301			0.744781
$186$	−16.6080	+	3.47733i	−1.21776	+	0.254970i
$187$	9.84851			0.720195
$188$	53.9156			3.93220
$189$	−13.4157	−	3.00324i	−0.975847	−	0.218453i
$190$	7.40587			0.537278
$191$	−23.1458			−1.67477			−0.837385	−	0.546614i	$-0.815916\pi$
$191$	−23.1458			−1.67477			−0.837385	+	0.546614i	$0.815916\pi$
$192$	23.8546	−	4.99458i	1.72156	−	0.360453i
$193$	4.29468			0.309138			0.154569	−	0.987982i	$-0.450601\pi$
$193$	4.29468			0.309138			0.154569	+	0.987982i	$0.450601\pi$
$194$	11.6171	−	20.1214i	0.834059	−	1.44463i
$195$	7.80365	−	1.63390i	0.558831	−	0.117006i
$196$	−3.79944	+	35.0335i	−0.271388	+	2.50240i
$197$	−14.7455			−1.05058			−0.525288	−	0.850924i	$-0.676042\pi$
$197$	−14.7455			−1.05058			−0.525288	+	0.850924i	$0.676042\pi$
$198$	34.1560	+	25.1350i	2.42736	+	1.78626i
$199$	11.1399	−	19.2949i	0.789687	−	1.36778i	−0.136472	−	0.990644i	$-0.543576\pi$
$199$	11.1399	−	19.2949i	0.789687	−	1.36778i	0.926159	−	0.377133i	$-0.123090\pi$
$200$	4.02356	+	6.96901i	0.284509	+	0.492784i
$201$	2.80831	−	0.587992i	0.198083	−	0.0414738i
$202$	8.70793	+	15.0826i	0.612688	+	1.06121i
$203$	−10.9617	+	2.31104i	−0.769363	+	0.162203i
$204$	−5.02541	+	15.3079i	−0.351849	+	1.07177i
$205$	3.19552			0.223185
$206$	−1.55015	+	2.68493i	−0.108004	+	0.187068i
$207$	0.565386	−	5.08141i	0.0392970	−	0.353183i
$208$	−25.9485	−	44.9441i	−1.79920	−	3.11631i
$209$	7.44144	−	12.8889i	0.514735	−	0.891547i
$210$	−11.1262	+	4.89119i	−0.767783	+	0.337524i
$211$	−10.6046	−	18.3677i	−0.730050	−	1.26448i	−0.956861	−	0.290545i	$-0.906164\pi$
$211$	−10.6046	−	18.3677i	−0.730050	−	1.26448i	0.226812	−	0.973939i	$-0.427170\pi$
$212$	8.79826	−	15.2390i	0.604267	−	1.04662i
$213$	−4.74550	+	0.993594i	−0.325156	+	0.0680799i
$214$	−18.0174	−	31.2070i	−1.23164	−	2.13327i
$215$	−4.34272	−	7.52182i	−0.296171	−	0.512984i
$216$	−34.0514	+	24.2677i	−2.31690	+	1.65120i
$217$	−6.52724	−	7.27340i	−0.443098	−	0.493750i
$218$	−5.13141	+	8.88787i	−0.347543	+	0.601963i
$219$	−1.56766	+	4.77524i	−0.105933	+	0.322681i
$220$	26.8313			1.80896
$221$	8.50567			0.572153
$222$	31.0326	+	34.6769i	2.08277	+	2.32736i
$223$	−10.5877	+	18.3384i	−0.709003	+	1.22803i	0.256225	+	0.966617i	$0.417521\pi$
$223$	−10.5877	+	18.3384i	−0.709003	+	1.22803i	−0.965227	+	0.261412i	$0.915812\pi$
$224$	24.3988	+	27.1880i	1.63022	+	1.81657i
$225$	−2.41627	−	1.77810i	−0.161084	−	0.118540i
$226$	−6.59857	−	11.4291i	−0.438931	−	0.760250i
$227$	5.17913	+	8.97051i	0.343751	+	0.595394i	0.985126	−	0.171834i	$-0.0549691\pi$
$227$	5.17913	+	8.97051i	0.343751	+	0.595394i	−0.641375	+	0.767227i	$0.721636\pi$
$228$	16.2366	+	18.1433i	1.07529	+	1.20157i
$229$	8.23346	−	14.2608i	0.544082	−	0.942378i	−0.454582	−	0.890705i	$-0.650211\pi$
$229$	8.23346	−	14.2608i	0.544082	−	0.942378i	0.998664	−	0.0516730i	$-0.0164554\pi$
$230$	−2.26001	−	3.91445i	−0.149021	−	0.258111i
$231$	−2.66718	+	24.2784i	−0.175488	+	1.59740i
$232$	−17.0367	+	29.5084i	−1.11851	+	1.93732i
$233$	−10.6402	−	18.4294i	−0.697063	−	1.20735i	−0.969480	−	0.245170i	$-0.921156\pi$
$233$	−10.6402	−	18.4294i	−0.697063	−	1.20735i	0.272417	−	0.962179i	$-0.412177\pi$
$234$	29.4988	+	21.7078i	1.92840	+	1.41909i
$235$	−5.35500	+	9.27513i	−0.349322	+	0.605043i
$236$	−9.71864			−0.632629
$237$	14.6655	−	3.07060i	0.952624	−	0.199457i
$238$	−12.6872	+	2.67481i	−0.822389	+	0.173382i
$239$	10.3537	+	17.9332i	0.669727	+	1.16000i	0.977980	+	0.208696i	$0.0669221\pi$
$239$	10.3537	+	17.9332i	0.669727	+	1.16000i	−0.308254	+	0.951304i	$0.599745\pi$
$240$	−6.09088	+	18.5534i	−0.393165	+	1.19762i
$241$	−3.38125	−	5.85649i	−0.217805	−	0.377250i	0.736332	−	0.676621i	$-0.236556\pi$
$241$	−3.38125	−	5.85649i	−0.217805	−	0.377250i	−0.954137	+	0.299371i	$0.903223\pi$
$242$	23.0840	−	39.9826i	1.48389	−	2.57018i
$243$	7.99885	−	13.3798i	0.513127	−	0.858313i
$244$	−14.5729			−0.932934
$245$	−5.64947	−	4.13322i	−0.360931	−	0.264061i
$246$	9.78916	+	10.9388i	0.624134	+	0.697430i
$247$	6.42680	−	11.1315i	0.408928	−	0.708283i
$248$	−29.7242			−1.88749
$249$	2.44372	−	7.44379i	0.154864	−	0.471731i
$250$	−2.65219			−0.167740
$251$	17.1080			1.07984			0.539922	−	0.841715i	$-0.318454\pi$
$251$	17.1080			1.07984			0.539922	+	0.841715i	$0.318454\pi$
$252$	−36.3758	−	16.5343i	−2.29146	−	1.04156i
$253$	−9.08345			−0.571072
$254$	−35.8866			−2.25172
$255$	−2.13429	−	2.38493i	−0.133654	−	0.149350i
$256$	−2.40338			−0.150211
$257$	10.0751	−	17.4506i	0.628470	−	1.08854i	−0.359389	−	0.933188i	$-0.617015\pi$
$257$	10.0751	−	17.4506i	0.628470	−	1.08854i	0.987859	−	0.155354i	$-0.0496517\pi$
$258$	12.4448	−	37.9082i	0.774782	−	2.36006i
$259$	−8.32437	+	25.4763i	−0.517251	+	1.58302i
$260$	23.1728			1.43712
$261$	1.40470	−	12.6248i	0.0869488	−	0.781454i
$262$	−4.95061	+	8.57472i	−0.305850	+	0.529748i
$263$	−8.78459	−	15.2154i	−0.541681	−	0.938219i	−0.998808	−	0.0488177i	$-0.984455\pi$
$263$	−8.78459	−	15.2154i	−0.541681	−	0.938219i	0.457127	−	0.889402i	$-0.348879\pi$
$264$	49.5399	+	55.3577i	3.04897	+	3.40703i
$265$	1.74772	+	3.02714i	0.107362	+	0.185956i
$266$	−6.08574	+	18.6250i	−0.373140	+	1.14197i
$267$	7.22928	+	8.07826i	0.442424	+	0.494381i
$268$	8.33922			0.509399
$269$	1.41595	−	2.45249i	0.0863318	−	0.149531i	−0.819626	−	0.572899i	$-0.805819\pi$
$269$	1.41595	−	2.45249i	0.0863318	−	0.149531i	0.905958	+	0.423368i	$0.139152\pi$
$270$	−1.31527	−	13.7183i	−0.0800448	−	0.834869i
$271$	10.8055	+	18.7157i	0.656387	+	1.13690i	0.981544	+	0.191235i	$0.0612494\pi$
$271$	10.8055	+	18.7157i	0.656387	+	1.13690i	−0.325157	+	0.945660i	$0.605417\pi$
$272$	−10.4163	+	18.0415i	−0.631580	+	1.09393i
$273$	−2.30352	+	20.9681i	−0.139415	+	1.26905i
$274$	3.08815	+	5.34882i	0.186562	+	0.323134i
$275$	−2.66493	+	4.61580i	−0.160701	+	0.278343i
$276$	4.63502	−	14.1187i	0.278996	−	0.849846i
$277$	−3.56193	−	6.16944i	−0.214015	−	0.370686i	0.738952	−	0.673758i	$-0.235321\pi$
$277$	−3.56193	−	6.16944i	−0.214015	−	0.370686i	−0.952968	+	0.303072i	$0.901988\pi$
$278$	7.75881	+	13.4387i	0.465343	+	0.805997i
$279$	10.1505	−	4.44543i	0.607696	−	0.266141i
$280$	−20.8327	+	4.39212i	−1.24499	+	0.262479i
$281$	0.0926995	−	0.160560i	0.00552999	−	0.00957822i	−0.863247	−	0.504781i	$-0.831573\pi$
$281$	0.0926995	−	0.160560i	0.00552999	−	0.00957822i	0.868777	+	0.495203i	$0.164906\pi$
$282$	−48.1547	+	10.0824i	−2.86757	+	0.600401i
$283$	32.5657			1.93583			0.967914	−	0.251281i	$-0.0808517\pi$
$283$	32.5657			1.93583			0.967914	+	0.251281i	$0.0808517\pi$
$284$	−14.0917			−0.836187
$285$	−4.73385	+	0.991155i	−0.280409	+	0.0587110i
$286$	32.5346	−	56.3516i	1.92381	−	3.33214i
$287$	−2.62590	+	8.03642i	−0.155002	+	0.474375i
$288$	−37.9427	+	16.6170i	−2.23579	+	0.979168i
$289$	6.79282	+	11.7655i	0.399578	+	0.692089i
$290$	−5.61499	−	9.72546i	−0.329724	−	0.571098i
$291$	−4.73276	+	14.4164i	−0.277439	+	0.845105i
$292$	−7.30390	+	12.6507i	−0.427428	+	0.740328i
$293$	0.0655256	+	0.113494i	0.00382805	+	0.00663037i	0.867933	−	0.496681i	$-0.165448\pi$
$293$	0.0655256	+	0.113494i	0.00382805	+	0.00663037i	−0.864105	+	0.503312i	$0.832115\pi$
$294$	−3.15795	−	32.0007i	−0.184176	−	1.86632i
$295$	0.965273	−	1.67190i	0.0562004	−	0.0973419i
$296$	40.7591	+	70.5969i	2.36908	+	4.10336i
$297$	−25.1965	−	11.4951i	−1.46205	−	0.667015i
$298$	4.02515	−	6.97177i	0.233171	−	0.403864i
$299$	−7.84493			−0.453684
$300$	−5.81465	−	6.49750i	−0.335709	−	0.375133i
$301$	22.4852	−	4.74051i	1.29603	−	0.273239i
$302$	4.34825	+	7.53139i	0.250214	+	0.433383i
$303$	−7.58469	−	8.47541i	−0.435729	−	0.486900i
$304$	15.7409	+	27.2640i	0.902801	+	1.56370i
$305$	1.44741	−	2.50698i	0.0828783	−	0.143549i
$306$	1.62581	−	14.6120i	0.0929414	−	0.835312i
$307$	18.9900			1.08382			0.541909	−	0.840437i	$-0.317702\pi$
$307$	18.9900			1.08382			0.541909	+	0.840437i	$0.317702\pi$
$308$	−22.0484	+	67.4780i	−1.25633	+	3.84492i
$309$	0.631523	−	1.92368i	0.0359261	−	0.109434i
$310$	4.89829	−	8.48408i	0.278204	−	0.481864i
$311$	1.81374			0.102848			0.0514238	−	0.998677i	$-0.483624\pi$
$311$	1.81374			0.102848			0.0514238	+	0.998677i	$0.483624\pi$
$312$	42.7851	+	47.8097i	2.42223	+	2.70669i
$313$	−12.5540			−0.709592			−0.354796	−	0.934944i	$-0.615450\pi$
$313$	−12.5540			−0.709592			−0.354796	+	0.934944i	$0.615450\pi$
$314$	−50.8315			−2.86859
$315$	6.45731	−	4.61553i	0.363828	−	0.260056i
$316$	43.5489			2.44982
$317$	−0.525106			−0.0294929			−0.0147464	−	0.999891i	$-0.504694\pi$
$317$	−0.525106			−0.0294929			−0.0147464	+	0.999891i	$0.504694\pi$
$318$	−5.00840	+	15.2561i	−0.280857	+	0.855517i
$319$	−22.5678			−1.26356
$320$	−7.03555	+	12.1859i	−0.393299	+	0.681214i
$321$	15.6933	+	17.5363i	0.875916	+	0.978780i
$322$	11.7016	−	2.46702i	0.652106	−	0.137482i
$323$	−5.15971			−0.287094
$324$	30.7243	−	33.2981i	1.70691	−	1.84989i
$325$	−2.30157	+	3.98643i	−0.127668	+	0.221128i
$326$	−13.6145	−	23.5810i	−0.754036	−	1.30603i
$327$	2.09052	−	6.36791i	0.115606	−	0.352146i
$328$	12.8574	+	22.2696i	0.709930	+	1.22963i
$329$	−18.9256	−	21.0891i	−1.04340	−	1.16268i
$330$	−23.9643	+	5.01756i	−1.31919	+	0.276208i
$331$	25.2637			1.38862			0.694308	−	0.719678i	$-0.255710\pi$
$331$	25.2637			1.38862			0.694308	+	0.719678i	$0.255710\pi$
$332$	11.3855	−	19.7203i	0.624863	−	1.08229i
$333$	−24.4771	−	18.0124i	−1.34133	−	0.987073i
$334$	−20.3068	−	35.1724i	−1.11114	−	1.92455i
$335$	−0.828267	+	1.43460i	−0.0452531	+	0.0783806i
$336$	−41.6548	−	30.5641i	−2.27246	−	1.66741i
$337$	−6.81813	−	11.8093i	−0.371407	−	0.643296i	0.618375	−	0.785883i	$-0.287791\pi$
$337$	−6.81813	−	11.8093i	−0.371407	−	0.643296i	−0.989782	+	0.142587i	$0.954458\pi$
$338$	10.8593	−	18.8088i	0.590666	−	1.02306i
$339$	5.74742	+	6.42238i	0.312157	+	0.348816i
$340$	−4.65104	−	8.05583i	−0.252238	−	0.436889i
$341$	−9.84362	−	17.0497i	−0.533062	−	0.923290i
$342$	−17.8946	−	13.1684i	−0.967627	−	0.712066i
$343$	15.0371	−	10.8114i	0.811925	−	0.583762i
$344$	34.9464	−	60.5290i	1.88419	−	3.26350i
$345$	1.96849	+	2.19966i	0.105980	+	0.118426i
$346$	−45.6762			−2.45557
$347$	−2.24042			−0.120272			−0.0601362	−	0.998190i	$-0.519153\pi$
$347$	−2.24042			−0.120272			−0.0601362	+	0.998190i	$0.519153\pi$
$348$	11.5157	−	35.0779i	0.617307	−	1.88037i
$349$	10.1506	−	17.5814i	0.543349	−	0.941108i	−0.455360	−	0.890308i	$-0.650489\pi$
$349$	10.1506	−	17.5814i	0.543349	−	0.941108i	0.998709	−	0.0508008i	$-0.0161774\pi$
$350$	2.17943	−	6.67001i	0.116495	−	0.356527i
$351$	−21.7610	−	9.92777i	−1.16151	−	0.529905i
$352$	36.7955	+	63.7317i	1.96121	+	3.39691i
$353$	−9.46659	−	16.3966i	−0.503856	−	0.872704i	−0.999990	−	0.00445791i	$-0.998581\pi$
$353$	−9.46659	−	16.3966i	−0.503856	−	0.872704i	0.496134	−	0.868246i	$-0.334752\pi$
$354$	8.68020	−	1.81743i	0.461347	−	0.0965951i
$355$	1.39961	−	2.42420i	0.0742837	−	0.128663i
$356$	15.7540	+	27.2868i	0.834962	+	1.44620i
$357$	7.75171	−	3.40772i	0.410264	−	0.180356i
$358$	33.9981	−	58.8864i	1.79685	−	3.11224i
$359$	3.31533	+	5.74231i	0.174976	+	0.303068i	0.940153	−	0.340752i	$-0.110682\pi$
$359$	3.31533	+	5.74231i	0.174976	+	0.303068i	−0.765177	+	0.643820i	$0.777348\pi$
$360$	2.66963	−	23.9933i	0.140702	−	1.26456i
$361$	5.60137	−	9.70187i	0.294809	−	0.510625i
$362$	54.8990			2.88543
$363$	−9.40431	+	28.6464i	−0.493598	+	1.50355i
$364$	−19.0421	+	58.2774i	−0.998080	+	3.05457i
$365$	−1.45087	−	2.51299i	−0.0759422	−	0.131536i
$366$	13.0158	−	2.72519i	0.680346	−	0.142448i
$367$	−4.10922	−	7.11738i	−0.214500	−	0.371524i	0.738618	−	0.674124i	$-0.235479\pi$
$367$	−4.10922	−	7.11738i	−0.214500	−	0.371524i	−0.953118	+	0.302600i	$0.902145\pi$
$368$	9.60712	−	16.6400i	0.500806	−	0.867421i
$369$	−7.72123	−	5.68197i	−0.401951	−	0.295791i
$370$	−26.8670			−1.39675
$371$	−9.04914	+	1.90781i	−0.469808	+	0.0990485i
$372$	31.5238	−	6.60032i	1.63443	−	0.342211i
$373$	3.48034	−	6.02813i	0.180205	−	0.312125i	−0.761745	−	0.647877i	$-0.775657\pi$
$373$	3.48034	−	6.02813i	0.180205	−	0.312125i	0.941950	+	0.335752i	$0.108990\pi$
$374$	−26.1202			−1.35064
$375$	1.69529	−	0.354953i	0.0875444	−	0.0183297i
$376$	−86.1847			−4.44464
$377$	−19.4907			−1.00382
$378$	35.5810	+	7.96516i	1.83009	+	0.409684i
$379$	−22.9048			−1.17654			−0.588271	−	0.808664i	$-0.700191\pi$
$379$	−22.9048			−1.17654			−0.588271	+	0.808664i	$0.700191\pi$
$380$	−14.0571			−0.721114
$381$	22.9388	−	4.80284i	1.17519	−	0.246057i
$382$	61.3871			3.14084
$383$	0.442401	−	0.766261i	0.0226056	−	0.0391541i	−0.854501	−	0.519449i	$-0.826137\pi$
$383$	0.442401	−	0.766261i	0.0226056	−	0.0391541i	0.877107	+	0.480295i	$0.159470\pi$
$384$	−16.4523	+	3.44472i	−0.839579	+	0.175788i
$385$	−9.41839	−	10.4950i	−0.480005	−	0.534877i
$386$	−11.3903			−0.579753
$387$	−2.88139	+	25.8965i	−0.146469	+	1.31639i
$388$	−22.0504	+	38.1925i	−1.11944	+	1.93893i
$389$	3.93497	+	6.81556i	0.199511	+	0.345563i	0.948370	−	0.317167i	$-0.102731\pi$
$389$	3.93497	+	6.81556i	0.199511	+	0.345563i	−0.748859	+	0.662729i	$0.769398\pi$
$390$	−20.6968	+	4.33342i	−1.04802	+	0.219431i
$391$	1.57456	+	2.72722i	0.0796290	+	0.137921i
$392$	6.07344	−	56.0015i	0.306755	−	2.82850i
$393$	2.01686	−	6.14354i	0.101737	−	0.309901i
$394$	39.1081			1.97024
$395$	−4.32536	+	7.49174i	−0.217632	+	0.376950i
$396$	−64.8315	−	47.7088i	−3.25791	−	2.39746i
$397$	−0.143168	−	0.247974i	−0.00718539	−	0.0124455i	0.862410	−	0.506210i	$-0.168954\pi$
$397$	−0.143168	−	0.247974i	−0.00718539	−	0.0124455i	−0.869596	+	0.493764i	$0.835621\pi$
$398$	−29.5452	+	51.1738i	−1.48097	+	2.56511i
$399$	1.39736	−	12.7197i	0.0699554	−	0.636779i
$400$	−5.63713	−	9.76380i	−0.281857	−	0.488190i
$401$	−11.9338	+	20.6700i	−0.595948	+	1.03221i	0.397464	+	0.917618i	$0.369890\pi$
$401$	−11.9338	+	20.6700i	−0.595948	+	1.03221i	−0.993412	+	0.114594i	$0.963443\pi$
$402$	−7.44817	+	1.55947i	−0.371481	+	0.0777793i
$403$	−8.50145	−	14.7249i	−0.423487	−	0.733502i
$404$	−16.5285	−	28.6283i	−0.822326	−	1.42431i
$405$	2.67670	+	8.59275i	0.133006	+	0.426977i
$406$	29.0727	−	6.12932i	1.44285	−	0.304193i
$407$	−26.9961	+	46.7585i	−1.33814	+	2.31773i
$408$	8.03317	−	24.4698i	0.397701	−	1.21144i
$409$	30.1206			1.48937			0.744684	−	0.667417i	$-0.232600\pi$
$409$	30.1206			1.48937			0.744684	+	0.667417i	$0.232600\pi$
$410$	−8.47514			−0.418557
$411$	−2.68980	−	3.00569i	−0.132678	−	0.148260i
$412$	2.94234	−	5.09628i	0.144959	−	0.251076i
$413$	3.41146	+	3.80145i	0.167867	+	0.187057i
$414$	−1.49951	+	13.4769i	−0.0736970	+	0.662353i
$415$	2.26167	+	3.91732i	0.111021	+	0.192294i
$416$	31.7784	+	55.0419i	1.55807	+	2.69865i
$417$	−6.75800	−	7.55163i	−0.330941	−	0.369805i
$418$	−19.7361	+	34.1840i	−0.965326	+	1.67199i
$419$	7.77995	+	13.4753i	0.380075	+	0.658310i	0.991073	−	0.133323i	$-0.0425647\pi$
$419$	7.77995	+	13.4753i	0.380075	+	0.658310i	−0.610997	+	0.791633i	$0.709231\pi$
$420$	21.1187	−	9.28399i	1.03049	−	0.453012i
$421$	−3.91870	+	6.78738i	−0.190986	+	0.330797i	−0.945577	−	0.325398i	$-0.894502\pi$
$421$	−3.91870	+	6.78738i	−0.190986	+	0.330797i	0.754591	+	0.656195i	$0.227835\pi$
$422$	28.1254	+	48.7147i	1.36912	+	2.37139i
$423$	29.4313	−	12.8895i	1.43100	−	0.626707i
$424$	−14.0641	+	24.3598i	−0.683014	+	1.18301i
$425$	1.84780			0.0896314
$426$	12.5860	−	2.63520i	0.609793	−	0.127676i
$427$	5.11542	+	5.70019i	0.247553	+	0.275852i
$428$	34.1989	+	59.2342i	1.65306	+	2.86319i
$429$	−13.2545	+	40.3743i	−0.639931	+	1.94929i
$430$	11.5177	+	19.9493i	0.555435	+	0.962042i
$431$	12.7498	−	22.0832i	0.614135	−	1.06371i	−0.376401	−	0.926457i	$-0.622838\pi$
$431$	12.7498	−	22.0832i	0.614135	−	1.06371i	0.990536	−	0.137256i	$-0.0438282\pi$
$432$	47.7070	−	33.9997i	2.29531	−	1.63581i
$433$	−8.97110			−0.431124			−0.215562	−	0.976490i	$-0.569158\pi$
$433$	−8.97110			−0.431124			−0.215562	+	0.976490i	$0.569158\pi$
$434$	17.3115	+	19.2905i	0.830979	+	0.925972i
$435$	4.89071	+	5.46506i	0.234492	+	0.262030i
$436$	9.73995	−	16.8701i	0.466459	−	0.807931i
$437$	4.75889			0.227649
$438$	4.15774	−	12.6649i	0.198664	−	0.605150i
$439$	19.0289			0.908202			0.454101	−	0.890950i	$-0.349961\pi$
$439$	19.0289			0.908202			0.454101	+	0.890950i	$0.349961\pi$
$440$	−42.8901			−2.04470
$441$	6.30135	+	20.0323i	0.300064	+	0.953919i
$442$	−22.5587			−1.07301
$443$	−15.7453			−0.748080			−0.374040	−	0.927413i	$-0.622028\pi$
$443$	−15.7453			−0.748080			−0.374040	+	0.927413i	$0.622028\pi$
$444$	−58.9030	−	65.8204i	−2.79541	−	3.12370i
$445$	−6.25888			−0.296699
$446$	28.0806	−	48.6370i	1.32965	−	2.30303i
$447$	−1.63983	+	4.99507i	−0.0775613	+	0.236259i
$448$	−24.8650	−	27.7075i	−1.17476	−	1.30905i
$449$	21.6017			1.01945			0.509724	−	0.860338i	$-0.329747\pi$
$449$	21.6017			1.01945			0.509724	+	0.860338i	$0.329747\pi$
$450$	6.40841	+	4.71588i	0.302095	+	0.222309i
$451$	−8.51584	+	14.7499i	−0.400995	+	0.694544i
$452$	12.5248	+	21.6935i	0.589115	+	1.02038i
$453$	−3.78737	−	4.23214i	−0.177946	−	0.198843i
$454$	−13.7361	−	23.7915i	−0.644665	−	1.11659i
$455$	−8.13419	−	9.06405i	−0.381337	−	0.424929i
$456$	−25.9543	−	29.0023i	−1.21542	−	1.35816i
$457$	−15.6619			−0.732631			−0.366316	−	0.930491i	$-0.619381\pi$
$457$	−15.6619			−0.732631			−0.366316	+	0.930491i	$0.619381\pi$
$458$	−21.8367	+	37.8223i	−1.02036	+	1.76732i
$459$	0.916356	+	9.55761i	0.0427718	+	0.446111i
$460$	4.28973	+	7.43003i	0.200010	+	0.346427i
$461$	3.47952	−	6.02671i	0.162057	−	0.280692i	−0.773549	−	0.633737i	$-0.781520\pi$
$461$	3.47952	−	6.02671i	0.162057	−	0.280692i	0.935606	+	0.353045i	$0.114854\pi$
$462$	7.07389	−	64.3911i	0.329107	−	2.99575i
$463$	−10.7588	−	18.6347i	−0.500002	−	0.866029i	−1.00000		2.55855e-6i	$-0.999999\pi$
$463$	−10.7588	−	18.6347i	−0.500002	−	0.866029i	0.499998	−	0.866027i	$-0.333334\pi$
$464$	23.8689	−	41.3421i	1.10808	−	1.91926i
$465$	−1.99554	+	6.07860i	−0.0925410	+	0.281889i
$466$	28.2199	+	48.8783i	1.30726	+	2.26424i
$467$	−4.46931	−	7.74107i	−0.206815	−	0.358214i	0.743895	−	0.668297i	$-0.232976\pi$
$467$	−4.46931	−	7.74107i	−0.206815	−	0.358214i	−0.950709	+	0.310083i	$0.899643\pi$
$468$	−55.9918	−	41.2037i	−2.58822	−	1.90464i
$469$	−2.92726	−	3.26189i	−0.135168	−	0.150620i
$470$	14.2025	−	24.5995i	0.655113	−	1.13469i
$471$	32.4916	−	6.80297i	1.49714	−	0.313464i
$472$	15.5353			0.715072
$473$	46.2922			2.12852
$474$	−38.8957	+	8.14382i	−1.78654	+	0.374058i
$475$	1.39618	−	2.41825i	0.0640610	−	0.110957i
$476$	24.0816	−	5.07707i	1.10378	−	0.232707i
$477$	1.15961	−	10.4220i	0.0530949	−	0.477191i
$478$	−27.4601	−	47.5623i	−1.25600	−	2.17545i
$479$	−4.19722	−	7.26979i	−0.191776	−	0.332165i	0.754063	−	0.656802i	$-0.228091\pi$
$479$	−4.19722	−	7.26979i	−0.191776	−	0.332165i	−0.945839	+	0.324637i	$0.894758\pi$
$480$	7.45934	−	22.7218i	0.340471	−	1.03711i
$481$	−23.3152	+	40.3830i	−1.06308	+	1.84131i
$482$	8.96772	+	15.5325i	0.408468	+	0.707488i
$483$	−7.14953	+	3.14300i	−0.325315	+	0.143011i
$484$	−43.8157	+	75.8910i	−1.99162	+	3.44959i
$485$	−4.38018	−	7.58670i	−0.198894	−	0.344494i
$486$	−21.2145	+	35.4858i	−0.962310	+	1.60967i
$487$	−16.5245	+	28.6212i	−0.748795	+	1.29695i	0.199605	+	0.979876i	$0.436034\pi$
$487$	−16.5245	+	28.6212i	−0.748795	+	1.29695i	−0.948401	+	0.317075i	$0.897299\pi$
$488$	23.2949			1.05451
$489$	11.8583	+	13.2509i	0.536253	+	0.599228i
$490$	14.9835	+	10.9621i	0.676885	+	0.495217i
$491$	−11.6636	−	20.2020i	−0.526371	−	0.911702i	−0.999528	−	0.0307237i	$-0.990219\pi$
$491$	−11.6636	−	20.2020i	−0.526371	−	0.911702i	0.473156	−	0.880978i	$-0.343115\pi$
$492$	−18.5808	−	20.7629i	−0.837688	−	0.936063i
$493$	3.91200	+	6.77578i	0.176188	+	0.305166i
$494$	−17.0451	+	29.5230i	−0.766896	+	1.32830i
$495$	14.6466	−	6.41447i	0.658313	−	0.288309i
$496$	41.6444			1.86989
$497$	4.94650	+	5.51196i	0.221881	+	0.247245i
$498$	−6.48121	+	19.7424i	−0.290430	+	0.884677i
$499$	3.89178	−	6.74077i	0.174220	−	0.301758i	−0.765671	−	0.643232i	$-0.777593\pi$
$499$	3.89178	−	6.74077i	0.174220	−	0.301758i	0.939891	+	0.341474i	$0.110926\pi$
$500$	5.03414			0.225133
$501$	17.6874	+	19.7645i	0.790215	+	0.883015i
$502$	−45.3736			−2.02512
$503$	−39.0069			−1.73923			−0.869615	−	0.493731i	$-0.835633\pi$
$503$	−39.0069			−1.73923			−0.869615	+	0.493731i	$0.835633\pi$
$504$	58.1471	+	26.4302i	2.59008	+	1.17730i
$505$	6.56659			0.292209
$506$	24.0911			1.07098
$507$	−4.42402	+	13.4760i	−0.196477	+	0.598489i
$508$	68.1164			3.02218
$509$	7.59474	−	13.1545i	0.336631	−	0.583062i	−0.647166	−	0.762349i	$-0.724046\pi$
$509$	7.59474	−	13.1545i	0.336631	−	0.583062i	0.983797	+	0.179287i	$0.0573791\pi$
$510$	5.66055	+	6.32530i	0.250653	+	0.280089i
$511$	7.51217	−	1.58377i	0.332319	−	0.0700620i
$512$	25.7837			1.13949
$513$	13.2006	+	6.02238i	0.582822	+	0.265895i
$514$	−26.7212	+	46.2825i	−1.17862	+	2.04143i
$515$	0.584477	+	1.01234i	0.0257551	+	0.0446092i
$516$	−23.6216	+	71.9536i	−1.03988	+	3.16758i
$517$	−28.5414	−	49.4352i	−1.25525	−	2.17416i
$518$	22.0778	−	67.5680i	0.970045	−	2.96877i
$519$	29.1964	−	6.11302i	1.28158	−	0.268332i
$520$	−37.0420			−1.62440
$521$	6.23269	−	10.7953i	0.273059	−	0.472952i	−0.696584	−	0.717475i	$-0.745298\pi$
$521$	6.23269	−	10.7953i	0.273059	−	0.472952i	0.969644	+	0.244522i	$0.0786312\pi$
$522$	−3.72554	+	33.4833i	−0.163062	+	1.46553i
$523$	18.6955	+	32.3816i	0.817499	+	1.41595i	0.907519	+	0.420010i	$0.137973\pi$
$523$	18.6955	+	32.3816i	0.817499	+	1.41595i	−0.0900202	+	0.995940i	$0.528693\pi$
$524$	9.39677	−	16.2757i	0.410500	−	0.711007i
$525$	−0.500423	+	4.55517i	−0.0218402	+	0.198804i
$526$	23.2985	+	40.3541i	1.01586	+	1.75952i
$527$	−3.41266	+	5.91091i	−0.148658	+	0.257483i
$528$	−69.4069	−	77.5578i	−3.02055	−	3.37527i
$529$	10.0478	+	17.4032i	0.436859	+	0.756662i
$530$	−4.63529	−	8.02856i	−0.201344	−	0.348739i
$531$	−5.30517	+	2.32341i	−0.230225	+	0.100827i
$532$	11.5513	−	35.3522i	0.500814	−	1.53271i
$533$	−7.35471	+	12.7387i	−0.318568	+	0.551776i
$534$	−19.1734	−	21.4251i	−0.829716	−	0.927155i
$535$	−13.5868			−0.587408
$536$	−13.3303			−0.575783
$537$	−13.8507	+	42.1904i	−0.597700	+	1.82065i
$538$	−3.75537	+	6.50449i	−0.161905	+	0.280428i
$539$	34.1335	−	15.0621i	1.47024	−	0.648769i
$540$	2.49652	+	26.0387i	0.107433	+	1.12053i
$541$	−11.9362	−	20.6741i	−0.513177	−	0.888849i	−0.999883	−	0.0152833i	$-0.995135\pi$
$541$	−11.9362	−	20.6741i	−0.513177	−	0.888849i	0.486706	−	0.873566i	$-0.338198\pi$
$542$	−28.6583	−	49.6376i	−1.23098	−	2.13212i
$543$	−35.0916	+	7.34734i	−1.50593	+	0.315305i
$544$	12.7565	−	22.0950i	0.546932	−	0.947315i
$545$	1.93478	+	3.35114i	0.0828769	+	0.143547i
$546$	6.10937	−	55.6114i	0.261457	−	2.37995i
$547$	17.3201	−	29.9993i	0.740554	−	1.28268i	−0.211690	−	0.977337i	$-0.567897\pi$
$547$	17.3201	−	29.9993i	0.740554	−	1.28268i	0.952243	−	0.305340i	$-0.0987701\pi$
$548$	−5.86162	−	10.1526i	−0.250396	−	0.433698i
$549$	−7.95500	+	3.48390i	−0.339511	+	0.148689i
$550$	7.06792	−	12.2420i	0.301377	−	0.522000i
$551$	11.8235			0.503696
$552$	−7.40913	+	22.5689i	−0.315354	+	0.960597i
$553$	−15.2867	−	17.0341i	−0.650055	−	0.724366i
$554$	9.44692	+	16.3625i	0.401361	+	0.695178i
$555$	17.1735	−	3.59572i	0.728974	−	0.152630i
$556$	−14.7270	−	25.5079i	−0.624565	−	1.08178i
$557$	−22.8043	+	39.4982i	−0.966249	+	1.67359i	−0.260029	+	0.965601i	$0.583732\pi$
$557$	−22.8043	+	39.4982i	−0.966249	+	1.67359i	−0.706221	+	0.707992i	$0.749601\pi$
$558$	−26.9212	+	11.7902i	−1.13966	+	0.499117i
$559$	39.9803			1.69099
$560$	29.1873	−	6.15349i	1.23339	−	0.260032i
$561$	16.6961	−	3.49576i	0.704909	−	0.147591i
$562$	−0.245857	+	0.425837i	−0.0103709	+	0.0179629i
$563$	3.90101			0.164408			0.0822039	−	0.996616i	$-0.473804\pi$
$563$	3.90101			0.164408			0.0822039	+	0.996616i	$0.473804\pi$
$564$	91.4026	−	19.1375i	3.84874	−	0.805835i
$565$	−4.97593			−0.209339
$566$	−86.3705			−3.63042
$567$	−23.8095	−	0.329415i	−0.999904	−	0.0138341i
$568$	22.5257			0.945158
$569$	26.8952			1.12751			0.563754	−	0.825943i	$-0.309357\pi$
$569$	26.8952			1.12751			0.563754	+	0.825943i	$0.309357\pi$
$570$	12.5551	−	2.62874i	0.525875	−	0.110106i
$571$	−31.4035			−1.31420			−0.657099	−	0.753805i	$-0.728217\pi$
$571$	−31.4035			−1.31420			−0.657099	+	0.753805i	$0.728217\pi$
$572$	−61.7540	+	106.961i	−2.58206	+	4.47227i
$573$	−39.2388	+	8.21566i	−1.63922	+	0.343214i
$574$	6.96440	−	21.3142i	0.290689	−	0.889636i
$575$	−1.70426			−0.0710724
$576$	38.6676	−	16.9345i	1.61115	−	0.705606i
$577$	19.5367	−	33.8386i	0.813324	−	1.40872i	−0.0972010	−	0.995265i	$-0.530989\pi$
$577$	19.5367	−	33.8386i	0.813324	−	1.40872i	0.910525	−	0.413454i	$-0.135678\pi$
$578$	−18.0159	−	31.2044i	−0.749362	−	1.29793i
$579$	7.28073	−	1.52441i	0.302577	−	0.0633524i
$580$	10.6578	+	18.4599i	0.442543	+	0.766506i
$581$	−11.7102	+	2.46884i	−0.485821	+	0.102425i
$582$	12.5522	−	38.2351i	0.520305	−	1.58490i
$583$	−18.6302			−0.771585
$584$	11.6754	−	20.2223i	0.483130	−	0.836806i
$585$	12.6495	−	5.53986i	0.522992	−	0.229045i
$586$	−0.173787	−	0.301007i	−0.00717906	−	0.0124345i
$587$	15.0916	−	26.1394i	0.622897	−	1.07889i	−0.366047	−	0.930596i	$-0.619289\pi$
$587$	15.0916	−	26.1394i	0.622897	−	1.07889i	0.988944	−	0.148293i	$-0.0473777\pi$
$588$	5.99412	+	60.7406i	0.247193	+	2.50490i
$589$	5.15715	+	8.93244i	0.212497	+	0.368055i
$590$	−2.56009	+	4.43421i	−0.105397	+	0.182554i
$591$	−24.9980	+	5.23398i	−1.02828	+	0.215297i
$592$	−57.1048	−	98.9084i	−2.34699	−	4.06511i
$593$	17.4563	+	30.2353i	0.716846	+	1.24161i	0.962243	+	0.272191i	$0.0877483\pi$
$593$	17.4563	+	30.2353i	0.716846	+	1.24161i	−0.245397	+	0.969423i	$0.578918\pi$
$594$	66.8260	+	30.4873i	2.74190	+	1.25091i
$595$	−1.51842	+	4.64703i	−0.0622491	+	0.190510i
$596$	−7.64015	+	13.2331i	−0.312953	+	0.542050i
$597$	12.0366	−	36.6645i	0.492625	−	1.50058i
$598$	20.8063			0.850832
$599$	30.2247			1.23495			0.617475	−	0.786591i	$-0.288156\pi$
$599$	30.2247			1.23495			0.617475	+	0.786591i	$0.288156\pi$
$600$	9.29478	+	10.3863i	0.379458	+	0.424020i
$601$	2.96737	−	5.13964i	0.121042	−	0.209650i	−0.799137	−	0.601149i	$-0.794710\pi$
$601$	2.96737	−	5.13964i	0.121042	−	0.209650i	0.920179	+	0.391499i	$0.128043\pi$
$602$	−59.6353	+	12.5728i	−2.43055	+	0.512428i
$603$	4.55218	−	1.99363i	0.185379	−	0.0811871i
$604$	−8.25342	−	14.2954i	−0.335827	−	0.581670i
$605$	−8.70372	−	15.0753i	−0.353856	−	0.612897i
$606$	20.1161	+	22.4784i	0.817160	+	0.913124i
$607$	4.67096	−	8.09034i	0.189588	−	0.328377i	−0.755525	−	0.655120i	$-0.772618\pi$
$607$	4.67096	−	8.09034i	0.189588	−	0.328377i	0.945113	+	0.326743i	$0.105951\pi$
$608$	−19.2774	−	33.3895i	−0.781803	−	1.35412i
$609$	−17.7630	+	7.80878i	−0.719794	+	0.316428i
$610$	−3.83881	+	6.64901i	−0.155429	+	0.269211i
$611$	−24.6498	−	42.6947i	−0.997225	−	1.72724i
$612$	−3.08595	+	27.7351i	−0.124742	+	1.12112i
$613$	8.04187	−	13.9289i	0.324808	−	0.562584i	−0.656665	−	0.754182i	$-0.728034\pi$
$613$	8.04187	−	13.9289i	0.324808	−	0.562584i	0.981473	+	0.191598i	$0.0613670\pi$
$614$	−50.3652			−2.03257
$615$	5.41733	−	1.13426i	0.218448	−	0.0457378i
$616$	35.2447	−	107.864i	1.42005	−	4.34598i
$617$	−19.2709	−	33.3781i	−0.775816	−	1.34375i	−0.934335	−	0.356397i	$-0.884005\pi$
$617$	−19.2709	−	33.3781i	−0.775816	−	1.34375i	0.158519	−	0.987356i	$-0.449328\pi$
$618$	−1.67492	+	5.10197i	−0.0673753	+	0.205231i
$619$	10.4162	+	18.0415i	0.418664	+	0.725148i	0.995805	−	0.0914967i	$-0.0291651\pi$
$619$	10.4162	+	18.0415i	0.418664	+	0.725148i	−0.577141	+	0.816644i	$0.695832\pi$
$620$	−9.29745	+	16.1037i	−0.373395	+	0.646738i
$621$	−0.845171	−	8.81515i	−0.0339155	−	0.353740i
$622$	−4.81039			−0.192879
$623$	5.14320	−	15.7405i	0.206058	−	0.630628i
$624$	−59.9433	−	66.9828i	−2.39965	−	2.68146i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	33.2956			1.33076
$627$	8.04042	−	24.4919i	0.321103	−	0.978111i
$628$	96.4834			3.85011
$629$	18.7184			0.746352
$630$	−17.1260	+	12.2413i	−0.682318	+	0.487704i
$631$	−13.3824			−0.532745			−0.266372	−	0.963870i	$-0.585825\pi$
$631$	−13.3824			−0.532745			−0.266372	+	0.963870i	$0.585825\pi$
$632$	−69.6133			−2.76907
$633$	−24.4975	−	27.3744i	−0.973689	−	1.08804i
$634$	1.39268			0.0553105
$635$	−6.76545	+	11.7181i	−0.268479	+	0.465019i
$636$	9.50646	−	28.9576i	0.376956	−	1.14824i
$637$	29.4794	−	13.0084i	1.16802	−	0.515410i
$638$	59.8543			2.36965
$639$	−7.69232	+	3.36886i	−0.304303	+	0.133270i
$640$	4.85236	−	8.40454i	0.191807	−	0.332219i
$641$	9.07821	+	15.7239i	0.358568	+	0.621058i	0.987722	−	0.156223i	$-0.0499319\pi$
$641$	9.07821	+	15.7239i	0.358568	+	0.621058i	−0.629154	+	0.777281i	$0.716599\pi$
$642$	−41.6218	−	46.5097i	−1.64268	−	1.83559i
$643$	−5.12873	−	8.88322i	−0.202257	−	0.350320i	0.746998	−	0.664826i	$-0.231494\pi$
$643$	−5.12873	−	8.88322i	−0.202257	−	0.350320i	−0.949255	+	0.314506i	$0.898161\pi$
$644$	−22.2109	+	4.68267i	−0.875231	+	0.184523i
$645$	−10.0321	−	11.2102i	−0.395012	−	0.441401i
$646$	13.6846			0.538412
$647$	−15.5836	+	26.9916i	−0.612654	+	1.06115i	0.378137	+	0.925750i	$0.376565\pi$
$647$	−15.5836	+	26.9916i	−0.612654	+	1.06115i	−0.990791	+	0.135399i	$0.956768\pi$
$648$	−49.1131	+	53.2274i	−1.92935	+	2.09097i
$649$	5.14477	+	8.91101i	0.201950	+	0.349788i
$650$	6.10421	−	10.5728i	0.239427	−	0.414699i
$651$	−13.6473	−	10.0137i	−0.534879	−	0.392466i
$652$	25.8417	+	44.7591i	1.01204	+	1.75290i
$653$	−4.47213	+	7.74595i	−0.175008	+	0.303122i	−0.940164	−	0.340722i	$-0.889328\pi$
$653$	−4.47213	+	7.74595i	−0.175008	+	0.303122i	0.765156	+	0.643845i	$0.222662\pi$
$654$	−5.54446	+	16.8889i	−0.216805	+	0.660409i
$655$	1.86661	+	3.23306i	0.0729345	+	0.126326i
$656$	−18.0136	−	31.2004i	−0.703312	−	1.21817i
$657$	−0.962653	+	8.65186i	−0.0375567	+	0.337541i
$658$	50.1944	+	55.9324i	1.95678	+	2.18047i
$659$	−9.44019	+	16.3509i	−0.367737	+	0.636940i	−0.989211	−	0.146495i	$-0.953201\pi$
$659$	−9.44019	+	16.3509i	−0.367737	+	0.636940i	0.621474	+	0.783435i	$0.286534\pi$
$660$	45.4868	−	9.52384i	1.77057	−	0.370715i
$661$	−3.47549			−0.135181			−0.0675904	−	0.997713i	$-0.521531\pi$
$661$	−3.47549			−0.135181			−0.0675904	+	0.997713i	$0.521531\pi$
$662$	−67.0041			−2.60419
$663$	14.4196	−	3.01912i	0.560010	−	0.117253i
$664$	−18.1999	+	31.5232i	−0.706294	+	1.22334i
$665$	4.93436	+	5.49844i	0.191346	+	0.213220i
$666$	64.9179	+	47.7724i	2.51552	+	1.85114i
$667$	−3.60810	−	6.24942i	−0.139706	−	0.241978i
$668$	38.5443	+	66.7608i	1.49133	+	2.58305i
$669$	−11.4399	+	34.8470i	−0.442292	+	1.34726i
$670$	2.19673	−	3.80484i	0.0848669	−	0.146994i
$671$	7.71449	+	13.3619i	0.297814	+	0.515830i
$672$	51.0136	+	37.4311i	1.96789	+	1.44394i
$673$	−2.80825	+	4.86403i	−0.108250	+	0.187495i	−0.915061	−	0.403314i	$-0.867858\pi$
$673$	−2.80825	+	4.86403i	−0.108250	+	0.187495i	0.806811	+	0.590809i	$0.201191\pi$
$674$	18.0830	+	31.3207i	0.696531	+	1.20643i
$675$	−4.72742	−	2.15674i	−0.181958	−	0.0830129i
$676$	−20.6120	+	35.7010i	−0.792769	+	1.37312i
$677$	16.8353			0.647035			0.323517	−	0.946222i	$-0.395135\pi$
$677$	16.8353			0.647035			0.323517	+	0.946222i	$0.395135\pi$
$678$	−15.2433	−	17.0334i	−0.585415	−	0.654164i
$679$	22.6792	−	4.78140i	0.870347	−	0.183493i
$680$	7.43473	+	12.8773i	0.285109	+	0.493823i
$681$	11.9642	+	13.3693i	0.458471	+	0.512312i
$682$	26.1072	+	45.2190i	0.999696	+	1.73152i
$683$	19.4914	−	33.7601i	0.745819	−	1.29180i	−0.203992	−	0.978972i	$-0.565392\pi$
$683$	19.4914	−	33.7601i	0.745819	−	1.29180i	0.949811	−	0.312824i	$-0.101275\pi$
$684$	33.9657	+	24.9950i	1.29871	+	0.955707i
$685$	2.32875			0.0889769
$686$	−39.8812	+	28.6740i	−1.52267	+	1.09478i
$687$	8.89619	−	27.0986i	0.339411	−	1.03388i
$688$	−48.9610	+	84.8029i	−1.86662	+	3.23308i
$689$	−16.0900			−0.612980
$690$	−5.22082	−	5.83393i	−0.198753	−	0.222094i
$691$	−9.23860			−0.351453			−0.175726	−	0.984439i	$-0.556227\pi$
$691$	−9.23860			−0.351453			−0.175726	+	0.984439i	$0.556227\pi$
$692$	86.6982			3.29577
$693$	4.09605	+	42.1057i	0.155596	+	1.59946i
$694$	5.94204			0.225557
$695$	5.85086			0.221936
$696$	−18.4080	+	56.0725i	−0.697753	+	2.12542i
$697$	5.90468			0.223656
$698$	−26.9214	+	46.6292i	−1.01899	+	1.76494i
$699$	−24.5798	−	27.4664i	−0.929694	−	1.03887i
$700$	−4.13678	+	12.6604i	−0.156355	+	0.478517i
$701$	−11.0745			−0.418277			−0.209138	−	0.977886i	$-0.567066\pi$
$701$	−11.0745			−0.418277			−0.209138	+	0.977886i	$0.567066\pi$
$702$	57.7143	+	26.3304i	2.17829	+	0.993776i
$703$	14.1434	−	24.4972i	0.533430	−	0.923928i
$704$	−37.4985	−	64.9494i	−1.41328	−	2.44787i
$705$	−5.78604	+	17.6248i	−0.217915	+	0.663789i
$706$	25.1072	+	43.4870i	0.944923	+	1.63666i
$707$	−5.39606	+	16.5143i	−0.202940	+	0.621085i
$708$	−16.4759	+	3.44966i	−0.619202	+	0.129646i
$709$	−46.7799			−1.75686			−0.878428	−	0.477874i	$-0.841408\pi$
$709$	−46.7799			−1.75686			−0.878428	+	0.477874i	$0.841408\pi$
$710$	−3.71204	+	6.42945i	−0.139311	+	0.241293i
$711$	23.7723	−	10.4111i	0.891531	−	0.390447i
$712$	−25.1830	−	43.6182i	−0.943772	−	1.63466i
$713$	3.14756	−	5.45173i	0.117877	−	0.204169i
$714$	−20.5590	+	9.03794i	−0.769403	+	0.338236i
$715$	−12.2670	−	21.2472i	−0.458762	−	0.794598i
$716$	−64.5318	+	111.772i	−2.41167	+	4.17713i
$717$	23.9180	+	26.7268i	0.893234	+	0.998132i
$718$	−8.79289	−	15.2297i	−0.328148	−	0.568369i
$719$	−13.6176	−	23.5865i	−0.507853	−	0.879626i	−0.999959	−	0.00909117i	$-0.997106\pi$
$719$	−13.6176	−	23.5865i	−0.507853	−	0.879626i	0.492106	−	0.870535i	$-0.336227\pi$
$720$	−3.74023	+	33.6153i	−0.139390	+	1.25277i
$721$	−3.02624	+	0.638015i	−0.112703	+	0.0237609i
$722$	−14.8559	+	25.7312i	−0.552881	+	0.957618i
$723$	−7.81097	−	8.72826i	−0.290493	−	0.324608i
$724$	−104.204			−3.87271
$725$	−4.23423			−0.157255
$726$	24.9421	−	75.9758i	0.925686	−	2.81973i
$727$	−11.4509	+	19.8335i	−0.424691	+	0.735586i	−0.996391	−	0.0848765i	$-0.972950\pi$
$727$	−11.4509	+	19.8335i	−0.424691	+	0.735586i	0.571701	+	0.820462i	$0.306284\pi$
$728$	30.4391	−	93.1571i	1.12815	−	3.45263i
$729$	8.81118	−	25.5218i	0.326340	−	0.945252i
$730$	3.84800	+	6.66493i	0.142421	+	0.246680i
$731$	−8.02448	−	13.8988i	−0.296796	−	0.514066i
$732$	−24.7053	+	5.17270i	−0.913134	+	0.191188i
$733$	2.51939	−	4.36370i	0.0930556	−	0.161177i	−0.815740	−	0.578419i	$-0.803670\pi$
$733$	2.51939	−	4.36370i	0.0930556	−	0.161177i	0.908795	+	0.417242i	$0.137003\pi$
$734$	10.8985	+	18.8767i	0.402269	+	0.696751i
$735$	−11.0446	−	5.00170i	−0.407386	−	0.184491i
$736$	−11.7656	+	20.3786i	−0.433685	+	0.751165i
$737$	−4.41455	−	7.64622i	−0.162612	−	0.281652i
$738$	20.4782	+	15.0697i	0.753813	+	0.554723i
$739$	−0.624198	+	1.08114i	−0.0229615	+	0.0397705i	−0.877278	−	0.479983i	$-0.840643\pi$
$739$	−0.624198	+	1.08114i	−0.0229615	+	0.0397705i	0.854316	+	0.519753i	$0.173976\pi$
$740$	50.9964			1.87466
$741$	6.94411	−	21.1524i	0.255098	−	0.777053i
$742$	24.0001	−	5.05988i	0.881071	−	0.185754i
$743$	16.1691	+	28.0058i	0.593189	+	1.02743i	0.993800	+	0.111185i	$0.0354645\pi$
$743$	16.1691	+	28.0058i	0.593189	+	1.02743i	−0.400611	+	0.916248i	$0.631202\pi$
$744$	−50.3911	+	10.5507i	−1.84743	+	0.386807i
$745$	−1.51767	−	2.62868i	−0.0556030	−	0.0963073i
$746$	−9.23055	+	15.9878i	−0.337954	+	0.585354i
$747$	1.50061	−	13.4868i	0.0549046	−	0.493456i
$748$	49.5788			1.81278
$749$	11.1649	−	34.1694i	0.407955	−	1.24852i
$750$	−4.49624	+	0.941405i	−0.164179	+	0.0343752i
$751$	−9.24906	+	16.0198i	−0.337503	+	0.584572i	−0.983962	−	0.178376i	$-0.942916\pi$
$751$	−9.24906	+	16.0198i	−0.337503	+	0.584572i	0.646459	+	0.762948i	$0.276249\pi$
$752$	120.747			4.40320
$753$	29.0029	−	6.07252i	1.05693	−	0.221295i
$754$	51.6932			1.88256
$755$	3.27898			0.119334
$756$	−67.5364	−	15.1187i	−2.45627	−	0.549862i
$757$	−35.5818			−1.29324			−0.646620	−	0.762812i	$-0.723818\pi$
$757$	−35.5818			−1.29324			−0.646620	+	0.762812i	$0.723818\pi$
$758$	60.7480			2.20647
$759$	−15.3991	+	3.22420i	−0.558951	+	0.117031i
$760$	22.4704			0.815088
$761$	−17.9862	+	31.1531i	−0.652001	+	1.12930i	0.330636	+	0.943758i	$0.392737\pi$
$761$	−17.9862	+	31.1531i	−0.652001	+	1.12930i	−0.982637	+	0.185540i	$0.940596\pi$
$762$	−60.8382	+	12.7381i	−2.20393	+	0.461451i
$763$	−10.0177	+	2.11200i	−0.362664	+	0.0764597i
$764$	−116.519			−4.21551
$765$	−4.46478	−	3.28558i	−0.161424	−	0.118790i
$766$	−1.17333	+	2.03227i	−0.0423943	+	0.0734291i
$767$	4.44329	+	7.69600i	0.160438	+	0.277886i
$768$	−4.07443	+	0.853088i	−0.147023	+	0.0307832i
$769$	22.7889	+	39.4715i	0.821788	+	1.42338i	0.904349	+	0.426793i	$0.140357\pi$
$769$	22.7889	+	39.4715i	0.821788	+	1.42338i	−0.0825609	+	0.996586i	$0.526310\pi$
$770$	24.9794	+	27.8349i	0.900195	+	1.00310i
$771$	10.8861	−	33.1601i	0.392054	−	1.19423i
$772$	21.6200			0.778122
$773$	20.8811	−	36.1671i	0.751040	−	1.30084i	−0.196279	−	0.980548i	$-0.562886\pi$
$773$	20.8811	−	36.1671i	0.751040	−	1.30084i	0.947319	−	0.320291i	$-0.103781\pi$
$774$	7.64201	−	68.6827i	0.274686	−	2.46875i
$775$	−1.84688	−	3.19889i	−0.0663419	−	0.114908i
$776$	35.2479	−	61.0511i	1.26532	−	2.19161i
$777$	−5.06934	+	46.1444i	−0.181862	+	1.65542i
$778$	−10.4363	−	18.0762i	−0.374159	−	0.648063i
$779$	4.46151	−	7.72757i	0.159850	−	0.276869i
$780$	39.2847	−	8.22527i	1.40662	−	0.294512i
$781$	7.45974	+	12.9207i	0.266931	+	0.462337i
$782$	−4.17604	−	7.23312i	−0.149335	−	0.258656i
$783$	−2.09983	−	21.9012i	−0.0750417	−	0.782687i
$784$	−8.50907	+	78.4598i	−0.303895	+	2.80213i
$785$	−9.58292	+	16.5981i	−0.342029	+	0.592412i
$786$	−5.34910	+	16.2939i	−0.190796	+	0.581183i
$787$	−23.9072			−0.852198			−0.426099	−	0.904677i	$-0.640112\pi$
$787$	−23.9072			−0.852198			−0.426099	+	0.904677i	$0.640112\pi$
$788$	−74.2311			−2.64437
$789$	−20.2932	−	22.6763i	−0.722456	−	0.807299i
$790$	11.4717	−	19.8695i	0.408144	−	0.706927i
$791$	4.08895	−	12.5140i	0.145386	−	0.444946i
$792$	103.634	+	76.2630i	3.68247	+	2.70989i
$793$	6.66262	+	11.5400i	0.236597	+	0.409797i
$794$	0.379709	+	0.657676i	0.0134754	+	0.0233400i
$795$	4.03739	+	4.51152i	0.143191	+	0.160007i
$796$	56.0798	−	97.1330i	1.98770	−	3.44279i
$797$	−18.7732	−	32.5161i	−0.664980	−	1.15178i	−0.979291	−	0.202459i	$-0.935107\pi$
$797$	−18.7732	−	32.5161i	−0.664980	−	1.15178i	0.314310	−	0.949320i	$-0.398227\pi$
$798$	−3.70607	+	33.7350i	−0.131193	+	1.19421i
$799$	−9.89496	+	17.1386i	−0.350059	+	0.606319i
$800$	6.90365	+	11.9575i	0.244081	+	0.422760i
$801$	15.1231	+	11.1289i	0.534349	+	0.393221i
$802$	31.6509	−	54.8209i	1.11763	−	1.93579i
$803$	15.4659			0.545781
$804$	14.1374	−	2.96003i	0.498588	−	0.104392i
$805$	1.40046	−	4.28604i	0.0493599	−	0.151063i
$806$	22.5475	+	39.0534i	0.794202	+	1.37560i
$807$	1.52992	−	4.66028i	0.0538558	−	0.164050i
$808$	26.4211	+	45.7626i	0.929490	+	1.60992i
$809$	−6.33279	+	10.9687i	−0.222649	+	0.385639i	−0.955612	−	0.294630i	$-0.904804\pi$
$809$	−6.33279	+	10.9687i	−0.222649	+	0.385639i	0.732963	+	0.680269i	$0.238137\pi$
$810$	−7.09912	−	22.7896i	−0.249438	−	0.800746i
$811$	−11.6090			−0.407649			−0.203824	−	0.979007i	$-0.565337\pi$
$811$	−11.6090			−0.407649			−0.203824	+	0.979007i	$0.565337\pi$
$812$	−55.1829	+	11.6341i	−1.93654	+	0.408276i
$813$	24.9616	+	27.8930i	0.875442	+	0.978251i
$814$	71.5988	−	124.013i	2.50954	−	4.34665i
$815$	−10.2666			−0.359622
$816$	−11.2547	+	34.2829i	−0.393994	+	1.20014i
$817$	−24.2529			−0.848500
$818$	−79.8857			−2.79314
$819$	3.53756	+	36.3646i	0.123612	+	1.27068i
$820$	16.0867			0.561771
$821$	22.7986			0.795676			0.397838	−	0.917456i	$-0.369761\pi$
$821$	22.7986			0.795676			0.397838	+	0.917456i	$0.369761\pi$
$822$	7.13388	+	7.97166i	0.248823	+	0.278044i
$823$	−2.60546			−0.0908205			−0.0454103	−	0.998968i	$-0.514460\pi$
$823$	−2.60546			−0.0908205			−0.0454103	+	0.998968i	$0.514460\pi$
$824$	−4.70336	+	8.14645i	−0.163849	+	0.283795i
$825$	−2.87944	+	8.77104i	−0.100249	+	0.305368i
$826$	−9.04787	−	10.0822i	−0.314816	−	0.350804i
$827$	24.3866			0.848004			0.424002	−	0.905661i	$-0.360625\pi$
$827$	24.3866			0.848004			0.424002	+	0.905661i	$0.360625\pi$
$828$	2.84623	−	25.5805i	0.0989133	−	0.888985i
$829$	3.13403	−	5.42830i	0.108849	−	0.188533i	−0.806455	−	0.591295i	$-0.798617\pi$
$829$	3.13403	−	5.42830i	0.108849	−	0.188533i	0.915304	+	0.402763i	$0.131950\pi$
$830$	−5.99838	−	10.3895i	−0.208207	−	0.360625i
$831$	−8.22836	−	9.19467i	−0.285439	−	0.318959i
$832$	−32.3856	−	56.0935i	−1.12277	−	1.94469i
$833$	−10.4391	−	7.63735i	−0.361693	−	0.264618i
$834$	17.9235	+	20.0284i	0.620641	+	0.693527i
$835$	−15.3132			−0.529935
$836$	37.4612	−	64.8847i	1.29562	−	2.24408i
$837$	15.6302	−	11.1393i	0.540257	−	0.385029i
$838$	−20.6339	−	35.7390i	−0.712787	−	1.23458i
$839$	0.469775	−	0.813675i	0.0162185	−	0.0280912i	−0.857802	−	0.513980i	$-0.828171\pi$
$839$	0.469775	−	0.813675i	0.0162185	−	0.0280912i	0.874021	+	0.485889i	$0.161504\pi$
$840$	−33.7585	+	14.8406i	−1.16478	+	0.512048i
$841$	5.53567	+	9.58806i	0.190885	+	0.330623i
$842$	10.3932	−	18.0015i	0.358172	−	0.620371i
$843$	0.100161	−	0.305100i	0.00344973	−	0.0105082i
$844$	−53.3849	−	92.4654i	−1.83759	−	3.18279i
$845$	−4.09444	−	7.09178i	−0.140853	−	0.243965i
$846$	−78.0574	+	34.1854i	−2.68367	+	1.17532i
$847$	45.0651	−	9.50097i	1.54846	−	0.326457i
$848$	19.7043	−	34.1288i	0.676647	−	1.17199i
$849$	55.2083	−	11.5593i	1.89474	−	0.396714i
$850$	−4.90072			−0.168093
$851$	−17.2643			−0.591813
$852$	−23.8895	+	5.00189i	−0.818440	+	0.171362i
$853$	−20.8291	+	36.0771i	−0.713175	+	1.23526i	0.250484	+	0.968121i	$0.419410\pi$
$853$	−20.8291	+	36.0771i	−0.713175	+	1.23526i	−0.963659	+	0.267134i	$0.913923\pi$
$854$	−13.5671	−	15.1180i	−0.464256	−	0.517328i
$855$	−7.67344	+	3.36059i	−0.262426	+	0.114930i
$856$	−54.6673	−	94.6865i	−1.86849	−	3.23632i
$857$	5.78245	+	10.0155i	0.197525	+	0.342123i	0.947725	−	0.319088i	$-0.103376\pi$
$857$	5.78245	+	10.0155i	0.197525	+	0.342123i	−0.750201	+	0.661210i	$0.770043\pi$
$858$	35.1534	−	107.081i	1.20012	−	3.65567i
$859$	−24.7429	+	42.8560i	−0.844217	+	1.46223i	0.0420825	+	0.999114i	$0.486601\pi$
$859$	−24.7429	+	42.8560i	−0.844217	+	1.46223i	−0.886299	+	0.463113i	$0.846733\pi$
$860$	−21.8619	−	37.8659i	−0.745483	−	1.29122i
$861$	−1.59911	+	14.5561i	−0.0544976	+	0.496072i
$862$	−33.8149	+	58.5691i	−1.15174	+	1.99487i
$863$	19.1330	+	33.1392i	0.651293	+	1.12807i	0.982809	+	0.184623i	$0.0591066\pi$
$863$	19.1330	+	33.1392i	0.651293	+	1.12807i	−0.331516	+	0.943450i	$0.607560\pi$
$864$	−58.4256	+	41.6386i	−1.98768	+	1.41657i
$865$	−8.61103	+	14.9147i	−0.292784	+	0.507116i
$866$	23.7931			0.808523
$867$	15.6920	+	17.5348i	0.532928	+	0.595514i
$868$	−32.8590	−	36.6153i	−1.11531	−	1.24280i
$869$	−23.0536	−	39.9299i	−0.782038	−	1.35453i
$870$	−12.9711	−	14.4944i	−0.439762	−	0.491406i
$871$	−3.81263	−	6.60367i	−0.129186	−	0.223757i
$872$	−15.5694	+	26.9670i	−0.527247	+	0.913218i
$873$	−2.90624	+	26.1199i	−0.0983614	+	0.884025i
$874$	−12.6215			−0.426929
$875$	−1.76710	−	1.96910i	−0.0597388	−	0.0665678i
$876$	−7.89181	+	24.0392i	−0.266640	+	0.812209i
$877$	−15.8817	+	27.5080i	−0.536288	+	0.928878i	0.462812	+	0.886456i	$0.346841\pi$
$877$	−15.8817	+	27.5080i	−0.536288	+	0.928878i	−0.999100	+	0.0424213i	$0.986493\pi$
$878$	−50.4684			−1.70323
$879$	0.151370	+	0.169146i	0.00510558	+	0.00570516i
$880$	60.0903			2.02564
$881$	28.5661			0.962416			0.481208	−	0.876606i	$-0.340198\pi$
$881$	28.5661			0.962416			0.481208	+	0.876606i	$0.340198\pi$
$882$	−16.7124	−	53.1296i	−0.562736	−	1.78897i
$883$	47.4172			1.59572			0.797858	−	0.602845i	$-0.205966\pi$
$883$	47.4172			1.59572			0.797858	+	0.602845i	$0.205966\pi$
$884$	42.8187			1.44015
$885$	1.04297	−	3.17699i	0.0350591	−	0.106793i
$886$	41.7595			1.40294
$887$	21.7767	−	37.7183i	0.731188	−	1.26646i	−0.225187	−	0.974316i	$-0.572299\pi$
$887$	21.7767	−	37.7183i	0.731188	−	1.26646i	0.956376	−	0.292140i	$-0.0943673\pi$
$888$	94.1571	+	105.215i	3.15971	+	3.53077i
$889$	−23.9104	−	26.6437i	−0.801930	−	0.893602i
$890$	16.5998			0.556425
$891$	−46.7956	−	10.5440i	−1.56771	−	0.353237i
$892$	−53.2998	+	92.3179i	−1.78461	+	3.09103i
$893$	14.9531	+	25.8995i	0.500385	+	0.866693i
$894$	4.34915	−	13.2479i	0.145457	−	0.443076i
$895$	−12.8188	−	22.2029i	−0.428486	−	0.742160i
$896$	17.1492	+	19.1096i	0.572915	+	0.638407i
$897$	−13.2994	+	2.78458i	−0.444055	+	0.0929745i
$898$	−57.2920			−1.91186
$899$	7.82011	−	13.5448i	0.260815	−	0.451745i
$900$	−12.1638	−	8.95122i	−0.405461	−	0.298374i
$901$	3.22943	+	5.59354i	0.107588	+	0.186348i
$902$	22.5857	−	39.1195i	0.752021	−	1.30254i
$903$	36.4364	−	16.0178i	1.21253	−	0.533038i
$904$	−20.0210	−	34.6773i	−0.665888	−	1.15335i
$905$	10.3497	−	17.9263i	0.344037	−	0.595889i
$906$	10.0448	+	11.2245i	0.333717	+	0.372908i
$907$	−13.1644	−	22.8015i	−0.437118	−	0.757110i	0.560348	−	0.828257i	$-0.310667\pi$
$907$	−13.1644	−	22.8015i	−0.437118	−	0.757110i	−0.997466	+	0.0711469i	$0.977334\pi$
$908$	26.0724	+	45.1588i	0.865244	+	1.49865i
$909$	−15.8666	−	11.6761i	−0.526263	−	0.387271i
$910$	21.5735	+	24.0396i	0.715153	+	0.796906i
$911$	2.76965	−	4.79718i	0.0917627	−	0.158938i	−0.816490	−	0.577359i	$-0.804083\pi$
$911$	2.76965	−	4.79718i	0.0917627	−	0.158938i	0.908253	+	0.418422i	$0.137417\pi$
$912$	36.3628	+	40.6331i	1.20409	+	1.34550i
$913$	−24.1088			−0.797884
$914$	41.5383			1.37397
$915$	1.56391	−	4.76383i	0.0517014	−	0.157487i
$916$	41.4484	−	71.7907i	1.36949	−	2.37203i
$917$	−9.66472	+	2.03759i	−0.319157	+	0.0672872i
$918$	−2.43035	−	25.3487i	−0.0802136	−	0.836630i
$919$	7.73926	+	13.4048i	0.255295	+	0.442183i	0.964975	−	0.262340i	$-0.0844942\pi$
$919$	7.73926	+	13.4048i	0.255295	+	0.442183i	−0.709681	+	0.704523i	$0.751161\pi$
$920$	−6.85718	−	11.8770i	−0.226075	−	0.391573i
$921$	32.1936	−	6.74056i	1.06081	−	0.222109i
$922$	−9.22837	+	15.9840i	−0.303920	+	0.526405i
$923$	6.44261	+	11.1589i	0.212061	+	0.367301i
$924$	−13.4270	+	122.221i	−0.441715	+	4.02077i
$925$	−5.06506	+	8.77294i	−0.166538	+	0.288452i
$926$	28.5343	+	49.4229i	0.937697	+	1.62414i
$927$	0.387799	−	3.48535i	0.0127370	−	0.114474i
$928$	−29.2316	+	50.6306i	−0.959574	+	1.66203i
$929$	−50.4021			−1.65364			−0.826820	−	0.562467i	$-0.809852\pi$
$929$	−50.4021			−1.65364			−0.826820	+	0.562467i	$0.809852\pi$
$930$	5.29257	−	16.1216i	0.173550	−	0.528650i
$931$	−17.8828	+	7.89114i	−0.586086	+	0.258622i
$932$	−53.5643	−	92.7760i	−1.75456	−	3.03898i
$933$	3.07481	−	0.643792i	0.100665	−	0.0210768i
$934$	11.8535	+	20.5308i	0.387858	+	0.671789i
$935$	−4.92426	+	8.52906i	−0.161040	+	0.278930i
$936$	89.5034	+	65.8645i	2.92551	+	2.15285i
$937$	−42.3109			−1.38224			−0.691118	−	0.722742i	$-0.742882\pi$
$937$	−42.3109			−1.38224			−0.691118	+	0.722742i	$0.742882\pi$
$938$	7.76366	+	8.65116i	0.253492	+	0.282470i
$939$	−21.2826	+	4.45607i	−0.694532	+	0.145418i
$940$	−26.9578	+	46.6923i	−0.879267	+	1.52293i
$941$	50.2654			1.63861			0.819303	−	0.573361i	$-0.194361\pi$
$941$	50.2654			1.63861			0.819303	+	0.573361i	$0.194361\pi$
$942$	−86.1742	+	18.0428i	−2.80771	+	0.587867i
$943$	−5.44599			−0.177346
$944$	−21.7655			−0.708406
$945$	9.30872	−	10.1167i	0.302813	−	0.329096i
$946$	−122.776			−3.99179
$947$	−44.6528			−1.45102			−0.725511	−	0.688210i	$-0.758397\pi$
$947$	−44.6528			−1.45102			−0.725511	+	0.688210i	$0.758397\pi$
$948$	73.8280	−	15.4578i	2.39782	−	0.502046i
$949$	13.3572			0.433592
$950$	−3.70294	+	6.41367i	−0.120139	+	0.208087i
$951$	−0.890206	+	0.186388i	−0.0288669	+	0.00604404i
$952$	−38.4947	+	8.11575i	−1.24762	+	0.263033i
$953$	21.3886			0.692845			0.346423	−	0.938079i	$-0.387396\pi$
$953$	21.3886			0.692845			0.346423	+	0.938079i	$0.387396\pi$
$954$	−3.07551	+	27.6412i	−0.0995733	+	0.894917i
$955$	11.5729	−	20.0448i	0.374490	−	0.648635i
$956$	52.1221	+	90.2781i	1.68575	+	2.91980i
$957$	−38.2590	+	8.01053i	−1.23674	+	0.258944i
$958$	11.1318	+	19.2809i	0.359653	+	0.622938i
$959$	−1.91364	+	5.85657i	−0.0617945	+	0.189119i
$960$	−7.60187	+	23.1560i	−0.245349	+	0.747356i
$961$	−17.3561			−0.559875
$962$	61.8363	−	107.104i	1.99368	−	3.45316i
$963$	32.8293	+	24.1587i	1.05791	+	0.778503i
$964$	−17.0217	−	29.4824i	−0.548230	−	0.949563i
$965$	−2.14734	+	3.71930i	−0.0691254	+	0.119729i
$966$	18.9620	−	8.33585i	0.610091	−	0.268202i
$967$	20.8575	+	36.1262i	0.670731	+	1.16174i	0.977697	+	0.210020i	$0.0673530\pi$
$967$	20.8575	+	36.1262i	0.670731	+	1.16174i	−0.306966	+	0.951721i	$0.599314\pi$
$968$	70.0399	−	121.313i	2.25117	−	3.89914i
$969$	−8.74721	+	1.83146i	−0.281001	+	0.0588348i
$970$	11.6171	+	20.1214i	0.373002	+	0.646059i
$971$	5.27744	+	9.14080i	0.169361	+	0.293342i	0.938195	−	0.346106i	$-0.112496\pi$
$971$	5.27744	+	9.14080i	0.169361	+	0.293342i	−0.768834	+	0.639448i	$0.779163\pi$
$972$	40.2673	−	67.3556i	1.29157	−	2.16043i
$973$	−4.80791	+	14.7143i	−0.154135	+	0.471720i
$974$	43.8261	−	75.9090i	1.40428	−	2.43228i
$975$	−2.48683	+	7.57511i	−0.0796423	+	0.242598i
$976$	−32.6369			−1.04468
$977$	3.80602			0.121765			0.0608827	−	0.998145i	$-0.480608\pi$
$977$	3.80602			0.121765			0.0608827	+	0.998145i	$0.480608\pi$
$978$	−31.4506	−	35.1441i	−1.00568	−	1.12378i
$979$	16.6795	−	28.8897i	0.533078	−	0.923319i
$980$	−28.4402	−	20.8072i	−0.908489	−	0.664661i
$981$	1.28372	−	11.5375i	0.0409861	−	0.368364i
$982$	30.9342	+	53.5796i	0.987149	+	1.70979i
$983$	1.38131	+	2.39251i	0.0440571	+	0.0763091i	0.887213	−	0.461360i	$-0.152638\pi$
$983$	1.38131	+	2.39251i	0.0440571	+	0.0763091i	−0.843156	+	0.537669i	$0.819305\pi$
$984$	29.7016	+	33.1897i	0.946854	+	1.05805i
$985$	7.37277	−	12.7700i	0.234916	−	0.406886i
$986$	−10.3754	−	17.9707i	−0.330419	−	0.572303i
$987$	−39.5701	−	29.0344i	−1.25953	−	0.924176i
$988$	32.3534	−	56.0377i	1.02930	−	1.78280i
$989$	7.40111	+	12.8191i	0.235342	+	0.407624i
$990$	−38.8455	+	17.0124i	−1.23459	+	0.540691i
$991$	11.8370	−	20.5022i	0.376013	−	0.651274i	−0.614465	−	0.788944i	$-0.710628\pi$
$991$	11.8370	−	20.5022i	0.376013	−	0.651274i	0.990478	+	0.137670i	$0.0439614\pi$
$992$	−51.0008			−1.61928
$993$	42.8292	−	8.96742i	1.35914	−	0.284572i
$994$	−13.1191	−	14.6188i	−0.416112	−	0.463680i
$995$	11.1399	+	19.2949i	0.353159	+	0.611689i
$996$	12.3020	−	37.4730i	0.389804	−	1.18738i
$997$	−15.2018	−	26.3302i	−0.481445	−	0.833886i	0.518329	−	0.855182i	$-0.326554\pi$
$997$	−15.2018	−	26.3302i	−0.481445	−	0.833886i	−0.999773	+	0.0212950i	$0.993221\pi$
$998$	−10.3218	+	17.8778i	−0.326730	+	0.565913i
$999$	−47.8893	−	21.8480i	−1.51515	−	0.691241i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.l.c.151.2	yes	36
3.2	odd	2		945.2.l.c.46.17		36
7.2	even	3		315.2.k.c.16.17	✓	36
9.4	even	3		315.2.k.c.256.17	yes	36
9.5	odd	6		945.2.k.c.361.2		36
21.2	odd	6		945.2.k.c.856.2		36
63.23	odd	6		945.2.l.c.226.17		36
63.58	even	3	inner	315.2.l.c.121.2	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.k.c.16.17	✓	36	7.2	even	3
315.2.k.c.256.17	yes	36	9.4	even	3
315.2.l.c.121.2	yes	36	63.58	even	3	inner
315.2.l.c.151.2	yes	36	1.1	even	1	trivial
945.2.k.c.361.2		36	9.5	odd	6
945.2.k.c.856.2		36	21.2	odd	6
945.2.l.c.46.17		36	3.2	odd	2
945.2.l.c.226.17		36	63.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.65219 q^{2} +(1.69529 - 0.354953i) q^{3} +5.03414 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-4.49624 + 0.941405i) q^{6} +(-1.76710 - 1.96910i) q^{7} -8.04712 q^{8} +(2.74802 - 1.20350i) q^{9} +O(q^{10})\)	\(q-2.65219 q^{2} +(1.69529 - 0.354953i) q^{3} +5.03414 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-4.49624 + 0.941405i) q^{6} +(-1.76710 - 1.96910i) q^{7} -8.04712 q^{8} +(2.74802 - 1.20350i) q^{9} +(1.32610 - 2.29687i) q^{10} +(-2.66493 - 4.61580i) q^{11} +(8.53432 - 1.78688i) q^{12} +(-2.30157 - 3.98643i) q^{13} +(4.68669 + 5.22244i) q^{14} +(-0.540247 + 1.64564i) q^{15} +11.2743 q^{16} +(-0.923899 + 1.60024i) q^{17} +(-7.28827 + 3.19191i) q^{18} +(1.39618 + 2.41825i) q^{19} +(-2.51707 + 4.35969i) q^{20} +(-3.69468 - 2.71096i) q^{21} +(7.06792 + 12.2420i) q^{22} +(0.852128 - 1.47593i) q^{23} +(-13.6422 + 2.85635i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(6.10421 + 10.5728i) q^{26} +(4.23150 - 3.01569i) q^{27} +(-8.89581 - 9.91273i) q^{28} +(2.11711 - 3.66695i) q^{29} +(1.43284 - 4.36456i) q^{30} +3.69376 q^{31} -13.8073 q^{32} +(-6.15622 - 6.87919i) q^{33} +(2.45036 - 4.24415i) q^{34} +(2.58884 - 0.545800i) q^{35} +(13.8339 - 6.05857i) q^{36} +(-5.06506 - 8.77294i) q^{37} +(-3.70294 - 6.41367i) q^{38} +(-5.31683 - 5.94121i) q^{39} +(4.02356 - 6.96901i) q^{40} +(-1.59776 - 2.76740i) q^{41} +(9.79902 + 7.19000i) q^{42} +(-4.34272 + 7.52182i) q^{43} +(-13.4156 - 23.2366i) q^{44} +(-0.331749 + 2.98160i) q^{45} +(-2.26001 + 3.91445i) q^{46} +10.7100 q^{47} +(19.1131 - 4.00183i) q^{48} +(-0.754734 + 6.95919i) q^{49} +(1.32610 + 2.29687i) q^{50} +(-0.998267 + 3.04081i) q^{51} +(-11.5864 - 20.0683i) q^{52} +(1.74772 - 3.02714i) q^{53} +(-11.2228 + 7.99821i) q^{54} +5.32986 q^{55} +(14.2200 + 15.8456i) q^{56} +(3.22529 + 3.60406i) q^{57} +(-5.61499 + 9.72546i) q^{58} -1.93055 q^{59} +(-2.71968 + 8.28438i) q^{60} -2.89482 q^{61} -9.79658 q^{62} +(-7.22582 - 3.28443i) q^{63} +14.0711 q^{64} +4.60314 q^{65} +(16.3275 + 18.2449i) q^{66} +1.65653 q^{67} +(-4.65104 + 8.05583i) q^{68} +(0.920719 - 2.80459i) q^{69} +(-6.86611 + 1.44757i) q^{70} -2.79922 q^{71} +(-22.1136 + 9.68469i) q^{72} +(-1.45087 + 2.51299i) q^{73} +(13.4335 + 23.2675i) q^{74} +(-1.15504 - 1.29069i) q^{75} +(7.02855 + 12.1738i) q^{76} +(-4.37979 + 13.4041i) q^{77} +(14.1013 + 15.7573i) q^{78} +8.65071 q^{79} +(-5.63713 + 9.76380i) q^{80} +(6.10319 - 6.61446i) q^{81} +(4.23757 + 7.33969i) q^{82} +(2.26167 - 3.91732i) q^{83} +(-18.5995 - 13.6474i) q^{84} +(-0.923899 - 1.60024i) q^{85} +(11.5177 - 19.9493i) q^{86} +(2.28753 - 6.96801i) q^{87} +(21.4450 + 37.1439i) q^{88} +(3.12944 + 5.42035i) q^{89} +(0.879863 - 7.90779i) q^{90} +(-3.78260 + 11.5764i) q^{91} +(4.28973 - 7.43003i) q^{92} +(6.26200 - 1.31111i) q^{93} -28.4050 q^{94} -2.79236 q^{95} +(-23.4074 + 4.90094i) q^{96} +(-4.38018 + 7.58670i) q^{97} +(2.00170 - 18.4571i) q^{98} +(-12.8784 - 9.47705i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9}+O(q^{10}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9	\( 36 q - q^{3} + 44 q^{4} - 18 q^{5} - 4 q^{6} - q^{7} - 9 q^{9} + q^{11} + 8 q^{12} + 2 q^{13} + 9 q^{14} - q^{15} + 60 q^{16} - 5 q^{17} - 21 q^{18} - 2 q^{19} - 22 q^{20} - 23 q^{21} - 19 q^{22} - 3 q^{23} - 32 q^{24} - 18 q^{25} - 4 q^{26} + 17 q^{27} + 5 q^{28} - 8 q^{29} + 2 q^{30} - 20 q^{32} - 35 q^{33} + 10 q^{34} - q^{35} - 44 q^{36} - 15 q^{37} - 22 q^{38} + 7 q^{39} - 4 q^{41} + 57 q^{42} - 29 q^{43} - 7 q^{44} + 6 q^{45} - 24 q^{46} + 46 q^{47} - 19 q^{48} - 7 q^{49} + 42 q^{51} - 7 q^{52} + 21 q^{54} - 2 q^{55} - 12 q^{56} + 21 q^{57} - 20 q^{58} + 10 q^{59} - 13 q^{60} + 6 q^{61} - 12 q^{62} + 2 q^{63} + 128 q^{64} - 4 q^{65} - 12 q^{66} + 70 q^{67} - 17 q^{68} - 50 q^{69} - 3 q^{70} + 24 q^{71} - 10 q^{72} - 10 q^{73} + 22 q^{74} + 2 q^{75} + 10 q^{76} + 35 q^{77} + 66 q^{78} + 56 q^{79} - 30 q^{80} - 49 q^{81} - 8 q^{82} - 22 q^{83} - 86 q^{84} - 5 q^{85} + 19 q^{86} - 42 q^{87} - 50 q^{88} - 4 q^{89} + 3 q^{90} + 7 q^{91} - 50 q^{92} - q^{93} + 4 q^{94} + 4 q^{95} - 179 q^{96} + 16 q^{97} + 16 q^{98} - 89 q^{99}+O(q^{100}) \) 36 * q - q^3 + 44 * q^4 - 18 * q^5 - 4 * q^6 - q^7 - 9 * q^9 + q^11 + 8 * q^12 + 2 * q^13 + 9 * q^14 - q^15 + 60 * q^16 - 5 * q^17 - 21 * q^18 - 2 * q^19 - 22 * q^20 - 23 * q^21 - 19 * q^22 - 3 * q^23 - 32 * q^24 - 18 * q^25 - 4 * q^26 + 17 * q^27 + 5 * q^28 - 8 * q^29 + 2 * q^30 - 20 * q^32 - 35 * q^33 + 10 * q^34 - q^35 - 44 * q^36 - 15 * q^37 - 22 * q^38 + 7 * q^39 - 4 * q^41 + 57 * q^42 - 29 * q^43 - 7 * q^44 + 6 * q^45 - 24 * q^46 + 46 * q^47 - 19 * q^48 - 7 * q^49 + 42 * q^51 - 7 * q^52 + 21 * q^54 - 2 * q^55 - 12 * q^56 + 21 * q^57 - 20 * q^58 + 10 * q^59 - 13 * q^60 + 6 * q^61 - 12 * q^62 + 2 * q^63 + 128 * q^64 - 4 * q^65 - 12 * q^66 + 70 * q^67 - 17 * q^68 - 50 * q^69 - 3 * q^70 + 24 * q^71 - 10 * q^72 - 10 * q^73 + 22 * q^74 + 2 * q^75 + 10 * q^76 + 35 * q^77 + 66 * q^78 + 56 * q^79 - 30 * q^80 - 49 * q^81 - 8 * q^82 - 22 * q^83 - 86 * q^84 - 5 * q^85 + 19 * q^86 - 42 * q^87 - 50 * q^88 - 4 * q^89 + 3 * q^90 + 7 * q^91 - 50 * q^92 - q^93 + 4 * q^94 + 4 * q^95 - 179 * q^96 + 16 * q^97 + 16 * q^98 - 89 * q^99

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